Search any question & find its solution
Question:
Answered & Verified by Expert
If $f(x)$ is a function such that $f^{\prime}(x)=(x-1)^{2}(4-x),$ then
Options:
Solution:
1281 Upvotes
Verified Answer
The correct answers are:
$f(x)$ is increasing in (0,3), $x=4$ is a critical point of $f(x)$
Given
$$
f^{\prime}(x)=(x-1)^{2}(4-x)
$$
The sign scheme of $f^{\prime}(x)$
Clearly. $f(x)$ is increasing, for $x \in(-\infty, 4)$ and decreasing, for $n \in(4, \infty)$
Since, $f^{\prime}(x)=0$ at $x=4$
$\mathrm{SO}, \mathrm{x}=4$ is a critical point.
$$
f^{\prime}(x)=(x-1)^{2}(4-x)
$$
The sign scheme of $f^{\prime}(x)$
Clearly. $f(x)$ is increasing, for $x \in(-\infty, 4)$ and decreasing, for $n \in(4, \infty)$
Since, $f^{\prime}(x)=0$ at $x=4$
$\mathrm{SO}, \mathrm{x}=4$ is a critical point.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.