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### Section 4-2 : Critical Points

Determine the critical points of each of the following functions.

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