Pauls Online Notes
Home / Calculus I / Applications of Derivatives / Finding Absolute Extrema
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

### Section 4-4 : Finding Absolute Extrema

For each of the following problems determine the absolute extrema of the given function on the specified interval.

1. $$f\left( x \right) = 8{x^3} + 81{x^2} - 42x - 8$$ on $$\left[ { - 8,2} \right]$$ Solution
2. $$f\left( x \right) = 8{x^3} + 81{x^2} - 42x - 8$$ on $$\left[ { - 4,2} \right]$$ Solution
3. $$R\left( t \right) = 1 + 80{t^3} + 5{t^4} - 2{t^5}$$ on $$\left[ { - 4.5,\,\,4} \right]$$ Solution
4. $$R\left( t \right) = 1 + 80{t^3} + 5{t^4} - 2{t^5}$$ on $$\left[ {0,7} \right]$$ Solution
5. $$h\left( z \right) = 4{z^3} - 3{z^2} + 9z + 12$$ on $$\left[ { - 2,1} \right]$$ Solution
6. $$g\left( x \right) = 3{x^4} - 26{x^3} + 60{x^2} - 11$$ on $$\left[ {1,5} \right]$$ Solution
7. $$Q\left( x \right) = {\left( {2 - 8x} \right)^4}{\left( {{x^2} - 9} \right)^3}$$ on $$\left[ { - 3,3} \right]$$ Solution
8. $$h\left( w \right) = 2{w^3}{\left( {w + 2} \right)^5}$$ on $$\left[ { - {\displaystyle \frac{5}{2}},{\displaystyle \frac{1}{2}}} \right]$$ Solution
9. $$\displaystyle f\left( z \right) = \frac{{z + 4}}{{2{z^2} + z + 8}}$$ on $$\left[ { - 10,0} \right]$$ Solution
10. $$A\left( t \right) = {t^2}\,{\left( {10 - t} \right)^{\frac{2}{3}}}$$ on $$\left[ {2,\,\,10.5} \right]$$ Solution
11. $$f\left( y \right) = \sin \left( {{\displaystyle \frac{y}{3}}} \right) + {\displaystyle \frac{2y}{9}}$$ on $$\left[ { - 10,15} \right]$$ Solution
12. $$g\left( w \right) = {{\bf{e}}^{{w^{\,3}} - 2{w^{\,2}} - 7w}}$$ on $$\left[ { - {\displaystyle \frac{1}{2}},\,\,{\displaystyle \frac{5}{2}}} \right]$$ Solution
13. $$R\left( x \right) = \ln \left( {{x^2} + 4x + 14} \right)$$ on $$\left[ { - 4,2} \right]$$ Solution