A curve has the slope dy/dx = 3√x for x > 0 and passes through the point (4, 20)…

Step 1. Integrate. $y = 3 \times \dfrac{x^{3/2}}{3/2} + C = 2x^{3/2} + C$.

Step 2. Use the point. At $x = 4$, $x^{3/2} = 8$, so $20 = 2 \times 8 + C$. Then $C = 4$.

Step 3. Evaluate. At $x = 9$, $x^{3/2} = 27$, so $y = 2 \times 27 + 4 = 58$.