Find the function whose derivative is y'=3x^2+5 and passes through the point (1,8).

Answer 1

Essentially it is asking you to find anti-derivative (indefinite integral) which is:

y = x^3 + 5x + C

You find C by plugging in the point (1,8):

8 = 1^3 +5*1 + C

So C = 2

The final answer is:

y = x^3 +5x + 2