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### 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 $$\left[ { - \frac{5}{2}},\frac{1}{2}}} \right$$ 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. $$f\left( y \right) = \sin \left( {\frac{y}{3}}} \right) + \frac{2y}{9}$$ on $$\left[ { - 10,15} \right]$$ Solution
12. $$g\left( w \right) = {{\bf{e}}^{{w^{\,3}} - 2{w^{\,2}} - 7w}}$$ on $$\left[ { - \frac{1}{2}},\,\,\frac{5}{2}}} \right$$ Solution
13. $$R\left( x \right) = \ln \left( {{x^2} + 4x + 14} \right)$$ on $$\left[ { - 4,2} \right]$$ Solution