IB Mathematics Analysis and Approaches 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 $[0,\frac{\pi }{2}]$, find the maximum and minimum values of the function $f(x)=\frac{\sin x}{e^x}$.

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 $$f(x)=x^4-4x^3+10.$$