Question

Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative. Remember to use absolute values where appropriate.) f(x) = 3 5 − 9 x , x > 0

Answer 1

`35x - (9x^2)/(2) + C`

Explanation:

The antiderivative of the function is the same as the integral. To find the integral or antiderivative, reverse the process of differentiation method. Currently the function has degree 1. Through integration we increase the degree of each term by 1 and divide by the degree.

Thus 35 - 9x becomes
`35x - (9x^2)/(2) + C`. We add a constant C for any possible constant that was eliminated during differentiation.