Find the interval in which the function $f(x) = x^4 - 4x^3 + 10$ is strictly decreasing.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $(-\infty, 0) \cup (0, 3)$ ##
We have $f(x) = x^4 - 4x^3 + 10$
$\Rightarrow f'(x) = 4x^3 - 12x^2$
$\Rightarrow f'(x) = 4x^2(x - 3)$
For $f(x)$ is strictly decreasing, we must have $f'(x) < 0$.
Value of $x$ is $0, 3$.
Hence, Strictly Decreasing in the interval $(-\infty, 0) \cup (0, 3)$.