Why are the ENDPOINTS tested in the Candidates Test?

At which values of $x$ does $q(x)=2x^3-6x^2$ take its absolute MINIMUM on $\left[-1,4\right]$?

At which value of $x$ does $r(x)={\left(x-1\right)}^{2/3}$ take its absolute MINIMUM on $\left[-4,4\right]$?

Find the absolute MAXIMUM VALUE of $u(x)=2x^3-3x^2$ on $\left[-4,6\right]$.

Find the absolute MAXIMUM VALUE of $v(x)=2x^3+15x^2+24x$ on $\left[-5,1\right]$.

At which value of $x$ does $w(x)={\left(x-3\right)}^{2/3}$ take its absolute MINIMUM on $\left[2,6\right]$?

Find the absolute MAXIMUM VALUE of $p(x)=2x^3+15x^2+36x$ on $\left[-4,4\right]$.

Find the absolute maximum VALUE of $f(x)=\cos x$ on $\left[\frac{\pi }{2},\frac{3\pi }{2}\right]$, with $x$ in radians.

Find the absolute MAXIMUM VALUE of $v(x)=2x^3-54x$ on $\left[-4,4\right]$.

Why does the Candidates Test require the interval to be CLOSED?

At which value of $x$ does $v(x)={\left(x+1\right)}^{2/3}$ take its absolute MINIMUM on $\left[-2,4\right]$?

Find the absolute MAXIMUM VALUE of $g(x)=2x^3+9x^2+12x$ on $\left[-5,4\right]$.

At which value of $x$ does $g(x)=2x^3-6x^2$ take its absolute MINIMUM on $\left[-2,5\right]$?

Find the absolute MAXIMUM VALUE of $q(x)=2x^3-9x^2+12x$ on $\left[-5,4\right]$.

A continuous function on $\left[a,b\right]$ has no critical points inside. Where are its absolute extrema?

At which value of $x$ does $q(x)={\left(x+2\right)}^{2/3}$ take its absolute MINIMUM on $\left[-3,2\right]$?

Find the absolute maximum VALUE of $f(x)=\ln x$ on $\left[1,e\right]$.

At which value of $x$ does $r(x)=2x^3-9x^2$ take its absolute MINIMUM on $\left[-3,4\right]$?

Find the absolute minimum VALUE of $f(x)=e^x-x$ on $\left[-1,1\right]$.

At which value of $x$ does $u(x)=2x^3+3x^2$ take its absolute MINIMUM on $\left[-5,6\right]$?

At which value of $x$ does $r(x)=2x^3-9x^2$ take its absolute MINIMUM on $\left[-1,6\right]$?

At which value of $x$ does $v(x)={\left(x-2\right)}^{2/3}$ take its absolute MINIMUM on $\left[1,4\right]$?

At which value of $x$ does $w(x)=2x^3+12x^2+18x$ take its absolute MINIMUM on $\left[-5,2\right]$?

Find the absolute minimum VALUE of $f(x)=x{e}^x$ on $\left[-2,1\right]$.

Find the absolute MAXIMUM VALUE of $p(x)=2x^3+12x^2+18x$ on $\left[-6,2\right]$.

At which value of $x$ does $s(x)=2x^3+18x^2+48x$ take its absolute MINIMUM on $\left[-6,4\right]$?

Find the absolute MAXIMUM VALUE of $p(x)=2x^3-15x^2+24x$ on $\left[-6,5\right]$.

Which hypothesis does the Extreme Value Theorem require of the function?

Find the absolute maximum VALUE of $f(x)=x-\ln x$ on $\left[\frac{1}{2},2\right]$.

Find the absolute MAXIMUM VALUE of $f(x)=2x^3+6x^2$ on $\left[-3,2\right]$.