Question

Find the greatest & the least values of the following functions in the given interval, if they exist. $y=x^5-5x^4+5x^3+1$ in $[-1,2]$

• A. $2$ & $-10$
• B. $3$ & $-10$
• C. $2$ & $10$
• D. none of these

Answer 1

Answer: (A)

$2$ & $-10$

Given, $y=x^5-5x^4+5x^3+1$

$\therefore y^{\prime }\left(x\right)=5x^4-20x^3+15x^2$
$=5x^2[x^2-4x+3]$
$=0$
$x=0,1,3$
Now $y\left(0\right)=1$ and $y\left(1\right)=2$
$3$ does not belong in the given range.
Now $y(-1)=10$
Hence, in the interval $[-1,2]$ it attains the maximum value , $y=2$ at $x=1$ and minimum value at $y=-10$, at $x=-1$.