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# NCERT Solutions for Class 12 Maths Application of Derivatives

Hi Students, Welcome to Amans Maths Blogs (AMB). In this post, you will get the NCERT Solutions for Class 12 Maths Application of Derivative Exercise 6.5.

CBSE Class 12th is an important school class in your life as you take some serious decision about your career. And out of all subjects, Maths is an important and core subjects. So CBSE NCERT Solutions for Class 12th Maths is major role in your exam preparation as it has detailed chapter wise solutions for all exercise. This NCERT Solutions can be downloaded in PDF file. The downloading link is given at last.

NCERT Solutions for Class 12 Maths are not only the solutions of Maths exercise but it builds your foundation of other important subjects. Getting knowledge of depth concept of CBSE Class 12th Maths like Algebra, Calculus, Trigonometry, Coordinate Geometry help you to understand the concept of Physics and Physical Chemistry.

As we know that all the schools affiliated from CBSE follow the NCERT books for all subjects. You can check the CBSE NCERT Syllabus. Thus, NCERT Solutions helps the students to solve the exercise questions as given in NCERT Books

The PDF books of NCERT Solutions for Class 12 are the first step towards the learning and understanding the each sections of Maths, Physics, Chemistry, Biology as it all help in engineering medical entrance exams. To solve it, you just need to click on download links of NCERT solutions for class 12.

NCERT Solutions for class 12 is highly recommended by the experienced teacher for students who are going to appear in CBSE Class 12 and JEE Mains and Advanced and NEET level exams. Here You will get NCERT Solutions for Class 12 Maths Application of Derivative Exercise 6.2 of all questions given in NCERT textbooks of class 12 in details with step by step process.

## NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5

NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 1.

Find the maximum and minimum values, if any, of the following functions given by

(i) f (x) = (2x – 1)2 + 3

NCERT Solutions: (ii) f (x) = 9x2 + 12x + 2

NCERT Solutions: (iii) f (x) = – (x – 1)2 + 10

NCERT Solutions: (iv) f (x) = x3 + 1

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 2.

Find the maximum and minimum values, if any, of the following functions given by

(i) f (x) = |x + 2 | – 1

NCERT Solutions: (ii) g(x) = – | x + 1| + 3

NCERT Solutions: (iii) h(x) = sin (2x) + 5

NCERT Solutions: (iv) f (x) = | sin 4x + 3|

NCERT Solutions: (v) h(x) = x + 1, x ∈ (– 1, 1)

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 3.

Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be:

(i) f (x) = x2

NCERT Solutions: (ii) g(x) = x3 – 3x

NCERT Solutions: (iii) h(x) = sin x + cos x, 0 < x < π/2.

NCERT Solutions: (iv) f (x) = sin x – cos x, 0 < x < 2π.

NCERT Solutions: (v) f (x) = x3 – 6x2 + 9x + 15

NCERT Solutions: (vi) g (x) = x/2 + 2/x, x > 0

NCERT Solutions: (vii) g (x) = 1/(x2 + 2)

NCERT Solutions: (viii) f (x) = x√(1 – x), x > 0

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 4.

Prove that the following functions do not have maxima or minima

(i) f (x) = ex

NCERT Solutions: (ii) g(x) = log x

NCERT Solutions: (iii) h (x) = x3 + x2 + x +1

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 5.

Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals:

(i) f (x) = x3, x ∈ [– 2, 2]

NCERT Solutions: (ii) f (x) = sin x + cos x , x ∈ [0, π]

NCERT Solutions: (iii) f (x) = 4x – x2/2 , x ∈ [-2, 9/2]

NCERT Solutions: (iv) f (x) = (x −1)2 + 3 , x ∈ [-3, 1]

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 6.

Find the maximum profit that a company can make, if the profit function is given by p(x) = 41 – 24x – 18x2

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 7.

Find both the maximum value and the minimum value of 3x4 – 8x3 + 12x2 – 48x + 25 on the interval [0, 3].

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 8.

At what points in the interval [0, 2π], does the function sin 2x attain its maximum value?

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 9.

What is the maximum value of the function sin x + cos x?

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 10.

Find the maximum value of 2x3 – 24x + 107 in the interval [1, 3]. Find the maximum value of the same function in [–3, –1].

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 11.

It is given that at x = 1, the function x4 – 62x2 + ax + 9 attains its maximum value, on the interval [0, 2]. Find the value of a.

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 12.

Find the maximum and minimum values of x + sin 2x on [0, 2π].

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 13.

Find two numbers whose sum is 24 and whose product is as large as possible.

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 14.

Find two positive numbers x and y such that x + y = 60 and xy3 is maximum.

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 15.

Find two positive numbers x and y such that their sum is 35 and the product x2y5 is a maximum.

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 16.

Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 17.

A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible.

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 18.

A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is maximum ?

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 19.

Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.

NCERT Solutions:  NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 20.

Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base.

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 21.

Of all the closed cylindrical cans (right circular), of a given volume of 100 cubic centimetres, find the dimensions of the can which has the minimum surface area?

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 22.

A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?

NCERT Solutions:  NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 23.

Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is 8/27 of the volume of the sphere.

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 24.

Show that the right circular cone of least curved surface and given volume has an altitude equal to √2 time the radius of the base.

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 25.

Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is tan-1√2.

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 26.

Show that semi-vertical angle of right circular cone of given surface area and maximum volume is sin-1(1/3).

NCERT Solutions: Choose the correct answer in the Exercises 27 and 29.

NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 27.

The point on the curve x2 = 2y which is nearest to the point (0, 5) is

(A) (2√2,4) (B) (2√2,0) (C) (0, 0) (D) (2, 2)

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 28.

For all real values of x, the minimum value of (1 – x + x2)/(1 + x + x2) is

(A) 0 (B) 1 (C) 3 (D) 1/3

NCERT Solutions: NCERT Solutions for Class 12 Maths Application of Derivatives Exercise 6.5: Ques No 29.

The maximum value of [x(x −1) +1]1/3, 0 ≤ x ≤ 1 is

(A) (1/3)1/3 (B) 1/2 (C) 1 (D) 0

NCERT Solutions: error: Content is protected !!