Question

What is the instantaneous rate of change of `f(x)=6x^2-3x` at `x=3`?

Answer 1

The instantaneous rate of change of `f(x)=6x^2-3x` at `x=3`
is `33`

Explanation:

Given:
`color(white)("XXX")f(x)=6x^2-3x`

`f'(color(blue)(x)) = 12color(blue)(x)-3`
and since the derivative is the slope of the tangent (the instantaneous rate of change) at the general value `x`

for `x=3`
`f'(color(blue)(3)) =12xxcolor(blue)(3) -3=33`