Question

find f(x) given f''(x) = 8 sqrtx

Answer 1

you need more information than that!

Answer 2

I know that I have to use antiderivatives and integration, but I don't know where to start.

Answer 3

you have the second derivative only
you can find the first derivative no problem
use the power rule backwards

Answer 4

can you integrate the first derivative to find f(x)?

Answer 5

sure, but your answer will have a \(Cx\) in it for some unknown \(C\)

Answer 6

f'(x) is sqrtx ^ 8 + C? I think that's the first derivative since if I work that in to the second it should give the second derivative.

Answer 7

or am i way off...

Answer 8

a bit off
the anti derivative of \(x^{\frac{1}{2}}\) is
\[\frac{x^{\frac{1}{2}+1}}{\frac{1}{2}+1}\] by using the powre ule backwards

Answer 9

aka \(\large \frac{2}{3}x^{\frac{3}{2}}\)

Answer 10

oh and i forgot your 8, so it should be
\[f'(x)=\frac{16}{3}x^{\frac{3}{2}}+C\]

Answer 11

\[\large
f''(x) = 8\sqrt{x} = 8x^{1/2} \\ \large
f'(x) = 8x^{3/2}*2/3 = 16/3 * x^{3/2} + C_1 \\ \large
f(x) = 16/3 * x^{5/2} * 2/5 + C_1x + C_2 \\ \large
f(x) = \frac{32}{15}x^{\frac 52} + C_1x + C_2
\]

Answer 12

Oh man, ok thanks for the help you two. I will need to let this soak in and see if I can work this out as well on my own. Cheers.