F(x) = −1.5x^6 − 2x^4 + 12x (a) Plot the function. (b) Use analytical methods to prove that the function is concave for all values of x. (c) Differentiate the function and then use a root-location method we learned previously to solve for the maximum f(x) and the corresponding value of x. (d) [15 pts] Solve for the value of x that maximizes x using the Golden-Section search method. Employ initial guesses of x = 0 and = 2 and perform three iterations. (e Solve for the value of xx that maximizes ff(xx) using Newton