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Question
Find the intervals in which the following functions are strictly increasing or decreasing:
10 − 6x − 2x2
Solution
It is known that- f(x) = 10 - 6x - 2x2
f'(x) = - 6 - 4x = - 2 (3 + 2x)
When f'(x) = 0 `=>` -2 (3 + 3x) = 0 `=> x = - 3/2`
The point `x = - 3/2` divides the number line into two parts, the intervals `(- infty, - 3/2)` and `(3/2, infty )`.
Interval `(- infty, - 3/2),` f'(x) = + Positive
Hence, the function f is continuously increasing
Interval `(3/2, infty),` f'(x) = - Positive
Hence, the function f is decreasing.
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