Question

Find f. Use C for the constant of the first anti derivative and d for the constant of the second derivative

Answer 1

we have the second derivative of the function f(x)

`f^(\doubleprime)(x)=2x+9e^x`

step 1

Find out the first antiderivative of the given function

`f^(\prime)(x)=\int 2x+9e^x=x^2+9e^x+C`

step 2

Find out the second antiderivative

`f(x)=\int x^2+9e^x+C=(x^3)/(3)+9e^x+Cx+D`

therefore

`f(x)=(x^3)/(3)+9e^x+Cx+D`