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y = f(x)

"slope at each point is 3*sqrt(x)" means that the derivative of F is 3*(x^.5)

since the derivative of a*(x^n) = a*n*(x^(n-1)) + c, we know that F = 2*(x^1.5) + c

To find C, look at 2*(9^1.5) + c = 4 and solve.

dy/dx = 3 sqrt(x)

dy = 3 sqrt(x) dx

Integrate both sides

dy = 3 x^(1/2) dx

y = (3) x^(1/2 +1) /(1/2 +1) + C

y = 3 (2/3) x^(3/2) + C

y = 2 x^(3/2) + C

x=9; y=4

4 = 2 (9)^(3/2) + C

4 = 2 ((9)^(1/2))^3 + C

4 = (2) (3)^3 + C

4 = 54 + C

C = -50

y = 2 x^(3/2) - 50

take the integral of f'(x) = 3√x, then solve for C at (9, 4)

f(x) = 2x^(3/2) - 50