Question

Let f(x)=square root (x). If the rate of change of f at x=c is twice its rate of change at x=1, then c=

Answer 1

Aren't I looking for the second derivative and just looking for f " (1)?

Answer 2

no.
I understand that as \[f(x)=\sqrt{x}\implies f'(x)={1\over 2\sqrt{x}}\\
f'(x=c)=2\times f'(x=1)\\
{1\over2\sqrt{c}}=2\times{1\over 2\sqrt{1}}
\]then solve for 'c'

Answer 3

rate of change = first derivative

Answer 4

no wonder I kept getting -1/4 when the key stated it is +1/4 thanks, I will redo the problem

Answer 5

thank you

Answer 6

you are welcome.