Find the intervals in which the function $f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 5$ is
(a) strictly increasing
(b) strictly decreasing.

Open in App

Solution

$f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 5$
$f^{'} (x) = 12 x^{3} - 12 x^{2} - 24 x = 12 x (x^{2} - x - 2)$
$f^{'} (x) = 12 x (x - 2) (x + 1)$
Put $f^{'} (x) = 0 \Rightarrow x = 0, - 1, 2$
Intervals are $(- \infty, - 1), (- 1, 0), (0, 2), (2, \infty)$ as shown in the table.
$f (x)$ is strictly increasing in $(- 1, 0) & (2, \infty)$ , and
$f (x)$ is strictly decreasing in $(- \infty, - 1) \cup (0, 2) .$

Suggest Corrections

Similar questions

f (x) = x^{2} - 6 x + 5

Find the intervals in which the function f given by $f (x) = 2 x^{3} - 3 x^{2} - 36 x + 7$ is

a) strictly increasing

b) strictly decreasing

Find the intervals in which the function f given by $f (x) = 2 x^{2} - 3 x$ is

a) strictly increasing

b) strictly decreasing

Find the intervals in which the function given by $f (x) = 4 x^{3} - 6 x^{2} - 72 x + 30$ is

i) Strictly increasing ii) Strictly decreasing

f (x) = 4 x^{3} - 6 x^{2} - 72 x + 30

Join BYJU'S Learning Program