Let f(x) = root x. If the rate of change of f at x = c is twice its rate of change at x=1, then c=...?
i have no idea what to do.
Hello,
the rate of change is calculated by the first derivative:
$\displaystyle f'(x)=\frac{df}{dx}=\frac{1}{2 \sqrt{x}}$
Now calculate f'(1) = 1/2. That means you know now the value of the rate of change at c: It is 1. Therefore solve the following equation for c:
$\displaystyle f'(c)=\frac{1}{2 \sqrt{c}}=1$. I've got $\displaystyle c=\frac{1}{4}$
EB