find the values of a and b if the function y=2x^3+ax^2+bx+36 has a local maximum when x=-4 and a local minimum when x=5

Answer 1

at both max and min, the derivative is zero, so

dy/dx = 6x^2 + 2ax + b
at x=-4,
96 - 8a + b = 0
at x=5
150 + 10a + b = 0
subtract them
54 + 16a = 0
a = - 27/8

sub that back into one of the above equations to find b