Determine the values of the constants α and β so that the function f (x) = x3 + αx2 + βx + δ may have a relative maximum at x = −3, and a relative minimum at x = 1.

Answer 1

For ease of typing, I will use
f(x) = x^3 + ax^2 + bx + c

take the derivative and the c will drop out
set this equal to zero, with x = -3 to get an equation in a and b
repeat with x = 1

you now have two equations in a and b, use your favourite grade 9 method to solve them