Question

Using only the values given in the table for the function , f(x) = x3-3x-2 , what is the interval of x-values over which the function is decreased

Answer 1

F(x) = x³ - 3x - 2
Differentiate f(x) with respect to x
F'(x) = 3x² - 3 = 3(x² - 1)
We know, any Function f(x) decrease s in interval [a, b] when f'(x) < 0
∴ f'(x) = 3(x² - 1) < 0
⇒ (x - 1)(x + 1) < 0
⇒ -1 < x < 1

Hence, function f(x) = x³ - 3x - 2 , is decreased in (-1, 1)