Consider the function

Question

Consider the function f(t) = 3t 2 − 7t. (a) Complete the equation below by writing an expression for the average rate of change of f(t) on the interval [2, u].

a) ∆f/ ∆t = _______

Use an appropriate limit process, together with your result in part (a), to compute the instantaneous rate of change of f(t) at t = 2. Do not use the basic derivative rules.

Answer 1

Average rate of change = [3u^2-7u-(3*2^2-7*2))/(u-2)

= (3u^2-7u+2)/(u-2)

f’(2)=lim_u>2[3u^2-7u+2)/(u-2)]=lim_u>2(3u-1)(u-2)/(u-2)=lim_u>2(3u-1)=5