Let q ( x ) = x^3 + 3 x^2 − 297 x + 7 . Find all values of x for which q ′ ( x ) = 0 .

Answer 1

First differentiate,

q'(x) = 3x² + 6x - 297

you want the values of x where q'(x) = 0

3x² + 6x - 297 = 0

this can be factored as (3x + 33)(x - 9) = 0

so, q'(x) = 0 at x = 9, -11