Please help with my antiderivative question??? PLZZZ

Question

Find the particular antiderivative of the following derivative that satisfies the given condition.

C'(x)=3x^2−5x​; C(0)=5,000

Answer 1

Hi Matt,

Not sure where you're getting stuck. Just use the Power Rule to integrate term by term, then use the initial condition to determine the constant of integration.

For example, suppose C'(x) = 6x^2 - 4x and C(0) = 1000. Then

C(x) = 2x^3 - 2x^2 + k

and setting x = 0 yields k = 1000, so

C(x) = 2x^3 - 2x^2 + 1000