Question

F’(x)= 1+3 square root x f(9)=68

Answer 1

Answer:

$f(x) = x + 2x^\frac{3}{2} + 5$

Step-by-step explanation:

I'm assuming the question here is asking for f(x)

The first step would be to find the antiderivative of f'(x)

$\int{1+3\sqrt{x}} \, dx = \int{1 + 3x^\frac{1}{2}} dx$

Apply the reverse power rule

$x + 2x^\frac{3}{2} + C$

Now solve for C when x = 9

$x + 2x^\frac{3}{2} + C = 68\\9 + 2(9)^\frac{3}{2} + C = 68\\9 + 2(27) + C = 68\\9 + 54 + C = 68\\63 + C = 68\\C = 5$

Now substitute into the antiderivative

$f(x) = x + 2x^\frac{3}{2} + 5$