Question

Find the function given that it satisfies f''(x)=36x^2+24x
and its graph has a horizontal tangent line at the point (0,1)
@calculus

Answer 1

Take the integral of the double derived function to get the first derivative. Find the constant C by using the fact that the first derivative must equal zero (horizontal tangent) at the point x = 0. Now that you have identified C, integrate again to find the original function. To find out what the new constant C is, solve the equation f(0) = 1.
Once C is found, you have the function satisfying all the given conditions.