Math Help - Rate of change

1. Rate of change

for the function f(x)=x^3 the rate of change at x=c is e^3 times the rate of change at x=2, what does c=?

2. Originally Posted by 333arizona
for the function f(x)=3x^2 the rate of change at x=c is e^3 times the rate of change at x=2, what does c=?
$f'(x)=6x$

so we know that $f'(c)=f'(2)\cdot{e^3}$

inputting our values we get

$6c=e^{3}\cdot{12}\Rightarrow{c=2e^{3}}$