Question

Let a function $f\left(x\right)=2x^3+5$ is defined in $[-1,1].$ Then the extremum value(s) of $f$ is/are

• A. $3$
• B. $5$
• C. $7$
• D. $f\left(x\right)$ has no extremum point.

Answer 1

Answer: (A), (C)

$7$

Plotting the graph of $f\left(x\right):$

as domain is $[-1,1].$

We can see that, $f(-1)<f(-1+h)$ as $h\to 0^{+}$
So, $f\left(x\right)$ has local minimum at $x=-1$
$\Rightarrow f(-1)=-2+5=3$ and
$f\left(1\right)>f(1-h)$ as $h\to 0^{+}$
So, $f\left(x\right)$ has local maximum at $x=1$
$\Rightarrow f\left(1\right)=7$