Question

The maximum value of $5+20x-4x^2$, when $x$ is a real number is

• A. $1$
• B. $5$
• C. $25$
• D. $30$

Answer 1

The correct option is A $1$

$f\left(x\right)=5+20-4x^2$

$f^{\prime }\left(x\right)=20-8x$

$f^{\prime }\left(x\right)=0$

$x=\frac{5}{2}$

If $x>\frac{5}{2}$, $f^{\prime }\left(x\right)<0$ $\Rightarrow f\left(x\right)$ is decreasing

If $x<\frac{5}{2}$, $f^{\prime }\left(x\right)>0$ $\Rightarrow f\left(x\right)$ is increasing.

At $\frac{5}{2}$ $f\left(x\right)$ has maxima

Maximum value$=f\left(5/2\right)=5+50-25=30$

$\therefore$Maximum value$=30$.