Question

Find f
f''(x)=1+3sqrt(x), f(4)=25

Answer 1

you need one more piece of information to do this

Answer 2

That's all I was given?

Answer 3

\[f''(x)=1+3\sqrt{x}\]
\[f'(x)=x+2x^{\frac{3}{2}}+c\]

Answer 4

you can't know \(c\) unless you know some value of \(f'\)

Answer 5

are you sure it isn't \[f'(x)=1+3\sqrt{x}\] find \(f(x)\)?

Answer 6

let me check again..

Answer 7

\[\int\limits_{?}^{?}1+3\sqrt{x}dx = x + 2x ^{3/2}+c\]
\[f(4)=25\rightarrow 25= 4+2(4)^{3/2}+c\]
\[25=4+16+c \rightarrow c=5\]
\[f(x)=x+2x ^{3/2}+5\]