Question

the instantaneous rate of change of y=f(x) with respect to x at x=2

Answer 1

What is f(x)?

Answer 2

f(x)=3x^2

Answer 3

Good deal.
Take the derivative of f(x) and then evaluate it at x=2, since instantaneous rate of change is just code for derivative. For f(x)=3x^2, f'(x) = 6x, so at x=2, the derivative is 12.

Answer 4

yeah i have the slope or rather the deritive, which infact is 12 smart,

Answer 5

f(x)=3x^2
f'(x)=6(x)
f'(2)=6*2=12

Answer 6

I'm just not sure, the definition of the instananeous rate of change is the lim as h -> 0 of the difference quotient, my professor did not explain this well

Answer 7

The lim as h -> 0 is the definition of the derivative. The derivative is the collecting instantaneous rates of change for the function f(x). So f'(x) at a point is that points instantaneous rate of change. Shanna and etothepiiplusone are correct.

Answer 8

thanks :)