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Question
Find the intervals in which the function f given by f(x) = 2x2 − 3x is
- strictly increasing
- strictly decreasing
Solution
f(x) = 2x2 - 3x
f'(x) = 4x - 3
If f'(x) = 0
4x - 3 = 0
x = `3/4`
(a) f'(x) = 4x - 3 > 0, x `in (3/4, infty)`
Therefore, the function is continuously increasing in `(3/4, infty)`.
(b) f'(x) = cos x < 0, x `in (- infty, 3/4)`
Therefore, the function is continuously decreasing in `(- infty, 3/4)`.
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