Intermediate First Year Mathematics Paper 1B>Chapter 10 - Applications of Derivatives>Exercise 10(h)>Q III

EASY

11th Andhra Pradesh Board

IMPORTANT

Earn 100

The profit function $P (x)$ of a company selling $x$ items per day is given by
$P (x) = (150 - x) x - 1000$ . Find the number of items that the company should manufacture to get maximum profit. Also find the maximum profit.

Important Questions on Applications of Derivatives

EASY

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 10 - Applications of Derivatives>Exercise 10(a)>Q II

Find the approximations of the following

\sqrt{82}

.(Answer up to

3

decimals)

MEDIUM

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 10 - Applications of Derivatives>Exercise 10(h)>Q III

Find the absolute maximum and absolute minimum of

f (x) = 8 x^{3} + 81 x^{2} - 42 x - 8

on

[- 8, 2]

EASY

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 10 - Applications of Derivatives>Exercise 10(h)>Q III

Find two positive integers whose sum is

16

and the sum of whose squares is minimum.

EASY

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 10 - Applications of Derivatives>Exercise 10(h)>Q III

Find two positive integers

x

and

y

such that

x + y = 60

and

x y^{3}

is maximum.

EASY

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 10 - Applications of Derivatives>Exercise 10(h)>Q III

From a rectangular sheet of dimensions

30 cm \times 80 cm

, four equal squares of side

x cm

, are removed at the corners, and the sides are then turned up so as to form an open rectangular box. Find the value of

x

, so that the volume of the box is the greatest.

EASY

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 10 - Applications of Derivatives>Exercise 10(h)>Q III

A window is in the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is

20 ft

, find the maximum area.

MEDIUM

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 10 - Applications of Derivatives>Exercise 10(h)>Q III

If the curved surface of right circular cylinder inscribed in a sphere of radius

R

is maximum, show that the height of the cylinder is

\sqrt{2} R

.

MEDIUM

11th Andhra Pradesh Board

IMPORTANT

Intermediate First Year Mathematics Paper 1B>Chapter 10 - Applications of Derivatives>Exercise 10(h)>Q III

A wire of length

l

is cut into two parts which are bead respectively in the form of a square and a circle. What are the lengths of the pieces of the wire respectively so that the sum of the areas is the least.