Answer
$f(x) = x + 2x^{\frac{3}{2}} + 5$
Work Step by Step
$f'(x) = 1 + 3x^{\frac{1}{2}}$
$f(x) = \int 1 + 3x^{\frac{1}{2}}dx$
$f(x) = x + \frac{3x^{\frac{1}{2}}}{\frac{3}{2}} + C$
$f(x) = x + 2x^{\frac{3}{2}} + C$
Given $f(4) = 25$:
$f(4) = 4 + 2(4)^{\frac{3}{2}} + C$
$f(4) = 4 + 2(8) + C$
$f(4) = 4 + 16 + C$
$25 = 20 + C$
$25 - 20 = C$
$5 = C$
Substitute:
$f(x) = x + 2x^{\frac{3}{2}} + 5$
