Question

Find the intervals in which the function f given by f(x) = 2x³ − 3x² − 36x + 7 is

(a) strictly increasing (b) strictly decreasing

Answer 1

The given function is f(x) = 2x³ − 3x² − 36x + 7.

∴ x = − 2, 3

The points x = −2 and x = 3 divide the real line into three disjoint intervals i.e.,

In intervalsis positive while in interval

(−2, 3), is negative.

Hence, the given function (f) is strictly increasing in intervals

, while function (f) is strictly decreasing in interval

(−2, 3).