Question

Identify the absolute extrema for the following function.
$f\left(x\right)=x^{2}on[-1,2]$

• A. Minima x = 0 & maxima x = 2
• B. Minima x = 2 & maxima x = 1
• C. Minima x = 3 & maxima x = 4
• D. Minima x = 1 & maxima x = 2

Answer 1

The correct option is A Minima x = 0 & maxima x = 2

$f\left(x\right)=x^2$ on $[-1,2]$

The function $x^2$ is continuous on $[-1,2]$. Now let us find the critical points of this function

$f^{\prime }\left(x\right)=2x=0\Rightarrow x=0$

So, we need to check function values at $0,-1$ & $2$

$f\left(0\right)=0,f(-1)=1,f\left(2\right)=4$

$minimaisatx=0maximaisatx=2$