Home > Calculus > Average Rate of Change Over an Interval

How do you find the average rate of change of the function #h(x) =sqrtx# over the given interval [16,49]?

Answer 1

Isaiah Allen

#(h(49)-h(16))/(49-16) = 1/11#

#(h(49)-h(16))/(49-16) = (sqrt(49)-sqrt(16))/(49-16)#

# = (7-4)/33 = 3/33 = 1/11#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Ezra Adams

To find the average rate of change of the function ( h(x) = \sqrt{x} ) over the interval ([16,49]), you calculate the difference in the function values at the endpoints of the interval and divide it by the difference in the x-values of those endpoints.

( h(49) = \sqrt{49} = 7 )
( h(16) = \sqrt{16} = 4 )

So, the change in the function values is (7 - 4 = 3).
The change in the x-values is (49 - 16 = 33).

Therefore, the average rate of change of ( h(x) = \sqrt{x} ) over the interval ([16,49]) is ( \frac{3}{33} = \frac{1}{11} ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.