F(x) = 2kx^3 + 3x^2 + px - 3 has a local minimum at x=-1 and a point of inflection at x = 1. Determine the values of K and P.
^ is the power to x number
Obviously I need first and second derivatives
F'(X) = 6kx^2 + 6x + p
F''(x) = 12kx + 6
But i am not sure where to move onto next. Step by step would be nice but I am sure I could figure it out if you posted any sort of help. +Rep to people who help me solve for tomorrow.
---- SOLVED
Solution
F"(x) = 12kx + 6
F"(1) = 12k(1) + 6
K = 1/2
F'(x) = 6kx^2 + 6x + p
F'(-1) = 6K(-1)^2 + 6(-1) + p
0= 6(.5)(-1) - 6 + p
0= 6(-.5) - 6 + p
0 = -3 -6 + p
9=p