# 4.1

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1. Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (If an answer does not exist, enter DNE.) f(t) = 3 cos t, -3pi/2 <= t <= 3pi/2
2. Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (If an answer does not exist, enter DNE.) f(t) =ln 5x, 0< x <= 7
3. Find the critical numbers of the function. (Enter your comma-separated list. If an answer does not exist, enter DNE.) f(x) = x^3 + 3x^2 – 189x
4. Find the critical numbers of the function. (Enter your comma-separated list. If an answer does not exist, enter DNE.) f(x) =8 x^3 – 12x^2 – 144x
5. Find the critical numbers of the function. (Enter your comma-separated list. If an answer does not exist, enter DNE.) f(x) = 4x^3 + x^2 + 4x
6. Find the critical numbers of the function. (Enter your comma-separated list. If an answer does not exist, enter DNE.) g(y) = y-1/y^2-3y+3
7. Find the critical numbers of the function. (Enter your comma-separated list. If an answer does not exist, enter DNE.) h(p) =p-1/p^2 +2
8. Find the critical numbers of the function. (Enter your comma-separated list. If an answer does not exist, enter DNE.) F(x) = x^4/5(x-9)^2
9. Find the critical numbers of the function. (Enter your comma-separated list. If an answer does not exist, enter DNE.) f(theta) = 14 cos theta + 7 sin^2 theta
10. Find the critical numbers of the function. (Enter your comma-separated list. If an answer does not exist, enter DNE.) f(x) = x^6e^-9x
11. Find the critical numbers of the function. (Enter your comma-separated list. If an answer does not exist, enter DNE.) f(x) = x^-2 ln x
12. Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = 4x^3 – 6x^2 – 144x + 9, [-4, 5]
13. Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = (x^2 – 1)^3, [-1, 5]
14. Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = x/x^2 – x + 9 , [0, 9]
15. Find the absolute maximum and absolute minimum values of f on the given interval.
f(t) = 16 cos t + 8 sin 2t , [0, pi/2]