Question

Let f(x) = sqrt(x)
If the rate of change of f at x=c is twice the rate of change at x=1, then c=
A) 1/4
B) 1
C) 4
D) 1/sqrt(2)
E) 1/2sqrt(2)

Answer 1

Have you studied derivatives yet?

Answer 2

Yes, a few chapters ago. This is on a review packet for our final and I just forget how to do it

Answer 3

f(x) = sqrt(x)

Answer 4

f'(x) =(1/2)x^-(1/2)

Answer 5

that is the rate of change or the derivative. Now substitute the value of 1 for x solve and then calculate twice to answer the problem.

Answer 6

I used the "power rule" to obtain the derivative.............remember how that went?
does this refresh your memory? ax^b the derivative would be abx^(b-1)

Answer 7

Yes the power rule I remember. I remember most of what we learned but I often have trouble just setting up the problem

Answer 8

Okay so I got f'(1) = 1/2.
So, since f'(x) is twice f'(1), the answer is 1. Correct?

Answer 9

For some unknown reason, I can't use the Equation or the Draw buttons beneath the box
Yes you are on the correct path.

Answer 10

sqrt(x)=x^(1/2)
the derivative would be 1/2x^-(1/2) which can be shown as 1/(2 sqrt x)

Answer 11

Yes I got that much..then subbing in I got f'(1) = 1/2.
2(f'(1)) = c so c =1. Is that the final answer?

Answer 12

I don't see any errors, good luck with your studies.

Answer 13

Thank you very much for your help!

Answer 14

you're welcome