Question

Let f(x)=root2x. If the rate of change of f at x=c is four times its rate of change at x=1 then c=?

Answer 1

`c=(1)/(16)`

Explanation:

`f(x)=√(2x)`

`f'(x)=(√(2x))/(2x)`

`f'(1)=(√(2))/(2)`

`f'(c)=(√(2c))/(2c)`

`f'(c)=4f'(1)`

`(√(2c))/(2c)=4((√(2))/(2))`

`(√(2c))/(2c)=2√(2)`

`√(2c)=4c√(2)`

`2c=32c^2`

`2=32c`

`(1)/(16)=c`