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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square increasing when the area of the square is 16  cm 2 ?

To determine

To find:

The rate at which area of square increases when area of square is 16cm2

Explanation

1. Concept:

Using the chain rule, we can find rate of change of area with respect to time in terms of rate of change of length of square with respect to time. By using area of square, we can find the length of side of square.

2. Formula:

i.

Area of square, A=(side length)2

ii. Power rule of differentiation:

ddxxn=n*xn-1

iii. Chain rule of differentiation:

ddtfx=ddxfx*dxdt

3. Given:

dsdt=6 cm/s,  A = 16 cm2

4. Calculations:

Let s the length of side of square.

Consider the area of square,A=s2

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