Question

I need help on #37!!

The function f(x)=x2 describes the area of the square, f(x), in square inches, whose sides each measure x inches. If x is changing.

a) find the average rate of change of the area with respect to x as x changes from 6 inches to 6.1 inches and from 6 inches to 6.01 inches.

b) Find the instantaneous rate of change of the area with respect to x at the moment when x = 6 inches


I could also use some advice for #39 but I think it’s similar to #37.

Answer 1

A) 12.1 , 12.01

B) infinitely large

Explanation:

Give that the function f(x)=x2 describes the area of the square, f(x), in square inches, whose sides each measure x inches. If x is changing.

Using the formula

(f(a + h) - f(a))/h

as x changes from 6 inches to 6.1 inches

a = 6, h = 0.1

= [f(6.1) - f(6)]/0.1

= (6.1^2 - 6^2)/0.1

= (37.21 - 36)/0.1

= 1.21/0.1

= 12.1

and when x changes from 6 inches to 6.01 inches.

a = 6, And h = 0.01

Using the same formula

(f(a + h) - f(a))/h

= [f(6.01) - f(6)]/0.01

= (6.01^2 - 6^2)/0.01

= (36.120 - 36)/0.01

=0.1201/0.01

= 12.01

B) the instantaneous rate of change of the area with respect to x at the moment when x = 6 inches is infinitely large since h = 0