Question

Maximum value of $(x+5{)}^4(13-x{)}^5$ is

• A. $7^4{.11}^5$
• B. $6^4{.14}^5$
• C. $8^4{.10}^5$
• D. $7^5{.10}^5$

Answer 1

The correct option is C $8^4{.10}^5$

$f^{\prime }\left(x\right)=4(x+5{)}^3(13-x{)}^5-5(x+5{)}^4(13-x{)}^4$
$4(x+5{)}^5(13-x{)}^5=5(x+5{)}^4(13-x{)}^4$
$4(13-x)=5(x+5)$
$27=9x$
$x=3$
When $f^1\left(x\right)=0$
$f^{\prime }\left(x\right)>0$ when $x<3$
$f^{\prime }\left(x\right)<0$ when $x>3$
So $f\left(x\right)$ is max as $x=3$
$f\left(3\right)=\left(8{)}^4\right(10{)}^5$