average rate of change of a function

Question

a function is given

f(t)=3sqrtT; t=a,t=a+h

Determine the average rate of change between the given values of the variable.

Answer 1

f(t) = 3sqrt

average rate of change from a to a+h

f(a) = 3sqra

f(a+h) = 3sqr(a+h)

average rate of change = change in f(t) over change in t

= (3sqr(a+h)- 3sqra)/h

this is not a limit problem.

had the problem asked for an "instantaneous" rate of change, that would be a limit problem

Answer 2

Set up the limit per the definition.

Multiply numerator and denominator by conjugate of numerator.

Take the limit.