Question

What is the instantaneous rate of change at x=2 of the function f given by f(x)= -x^3 +(3/5x^2) -4x? Step by step if possible.

Answer 1

what is another name for the instantaneous rate of change at a point?

Answer 2

what does it tell us we need to do that is

Answer 3

It's the limit of average rates of change over an interval as the interval shrinks around a point

Answer 4

right, and we call that a derivative

Answer 5

the "step by step" part isnt specific as far as how you need to go about this

Answer 6

there is the short and easy way, and then there is the long and drawn out way

Answer 7

So I just take the derivative and plug in 2 for x?

Answer 8

the short and easy way is:

f(x)= -x^3 +(3/5)x^2 -4x

f'(x)= -3x^2 +(6/5)x -4

f'(2) = -3(2)^2 +(6(2)/5) -4

f'(2) = -16 +(12/5)

yep

Answer 9

what is the slope of the tangent line at the point where x=2?

f'(2) of course