Question

let fx=sqrt x. the rate of chance of f at x=c is twice its rate of change at x=1, then c=?

Answer 1

try f'(c) = 2 * f'(1)

Answer 2

to find rate of change, take a derivative

f'(x)

then set up the equation "the derivative at x = c is twice the derivative at x = 1"

f'(c) = 2 * f'(1)

Answer 3

is the answer 1 or 1/4

Answer 4

let me see

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

f'(c) = 1/(2 sqrt c)
f'(1) = 1/2

f'(c) = 2 * f'(1) = 2 * 1/2 = 1
f'(c) = 1 = 1/ (2 sqrt c)
2 sqrt c = 1
sqrt c = 1/2
c = 1/4
yes