Question Type 4: Finding maxima and minima of a function on a closed interval Exercises

Determine the absolute extrema of $f(x)=e^x(2-x)$ on $[0,3]$.

Find the absolute maximum and minimum values of the function $f(x)=x^2$ on the interval $[-1,2]$.

Determine the absolute extrema of $f(x)=\frac{\ln x}{x}$ on the interval $[1,e]$.

Find the absolute extrema of $f(x) = \sin x$ on the closed interval $[0, \pi]$.

On the interval $[0,\dfrac{\pi}{2}]$, find the maximum and minimum values of the function $f(x)=\dfrac{\sin x}{e^x}$.

Determine the absolute maximum and minimum of $f(x)=x^3-3x^2+1$ on the interval $[-1,3]$.

Find the absolute maximum and minimum of the function $f(x) = x e^{-x}$ on the interval $[0, 4]$.

Find the absolute maximum and minimum values of the function $f(x)=\frac{x}{1+x^2}$ on the interval $[0,3]$.

Find the absolute maximum and minimum of $f(x)=\sin(2x)$ on the interval $[0,\pi]$.

Find the absolute maximum and minimum values of $f(x)=e^{-x^2}$ on the interval $[-2, 2]$.

On $[0,3]$, find the absolute extrema of the function $f(x)=x^2 e^{-x}$.

On the interval $[0,3]$, find the absolute maximum and minimum of the function $f(x)=x^4-4x^3+10.$