instantaneous rate of change of function y=f(t)

Question

anonymous · Answer

f(t) = t^3 - 1, t=2

lgbasallote · Answer

the rate of change is just the derivative right?

anonymous · Answer

i think so... like the lim as x approaches 0 of [f(x+h)-F(x)]/ h

anonymous · Answer

i keep getting stuck near the end

lgbasallote · Answer

do you know how to take the derivative? or you just know that limit definition?

anonymous · Answer

i know how to take the derivitive too can i use that in this situation?

lgbasallote · Answer

yes

lgbasallote · Answer

it's much faster than limits

anonymous · Answer

could you tell me what the answer is so when i finish my work i can refer back please?

lgbasallote · Answer

you can just tell me your answer and i'll tell you if it's wrong or not

lgbasallote · Answer

anyway...just so you have an idea

1. derive t^3 - 1

2. after you take the derivative, substitute 2 into t

3. simplify

4. ^answer to that is the final answer

lgbasallote · Answer

if that's what you did, and you used a calculator for the arithmetic part, then your final answer would be right. It's a straightforward solution so i doubt you'll get confused anywhere

anonymous · Answer

3t^2?

anonymous · Answer

so then at t=2, the instantaneous rate of change is 12?