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

EASY

11th Andhra Pradesh Board

IMPORTANT

Earn 100

Use the second derivative test to find local extrema of the function $f (x) = x^{3} - 9 x^{2} - 48 x + 72$ on $ℝ$ .

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(h)>Q II

Use the second derivative test to find local extrema of the function

f (x) = - x^{3} + 12 x^{2} - 5

on

ℝ

.

EASY

11th Andhra Pradesh Board

IMPORTANT

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

Find local maximum or local minimum of

f (x) = - \sin 2 x - x

defined on

[- \frac{π}{2}, \frac{π}{2}]

MEDIUM

11th Andhra Pradesh Board

IMPORTANT

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

Find the absolute maximum and absolute minimum of

f (x) = 2 x^{3} - 3 x^{2} - 36 x + 2

on the interval

[0, 5]

MEDIUM

11th Andhra Pradesh Board

IMPORTANT

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

Find the absolute extrema of

f (x) = 4 x - \frac{x^{2}}{2}

on

[- 2, \frac{9}{2}]

.

EASY

11th Andhra Pradesh Board

IMPORTANT

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

Find the maximum profit that a company can make, if the profit function is given by

P (x) = - 41 + 72 x - 18 x^{2}

EASY

11th Andhra Pradesh Board

IMPORTANT

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

The profit function

P (x)

of a company selling

x

items is given by

P (x) = - x^{3} + 9 x^{2} - 15 x - 13

where

x

represents units in thousands. Find the absolute maximum profit if the company can manufacture a maximum of

6000

units.

EASY

11th Andhra Pradesh Board

IMPORTANT

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

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.

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]