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2.7 Topics: The Extreme Value Theorem (EVT)
Find the critical numbers for the given function and then evaluate the ORIGINAL FUNCTION at the critical number.
1. f  x  
x2
x2  4
2
2. g  x    x  2  3
3. h  x   x3  3x2
4. k  x   sin 2 x  cos x
0  x  2
Locate the Absolute Extrema  x, y  and the Relative Extrema  x, y  of the given function on the closed interval.
5. f  x   x2  2x
2
1,1
6. y  3x 3  2 x
7. g  x  
x2
x 3
2
0, 4
 1,1
 1
8. h  x   cos  x 0, 
 6
9. y  ex sin x
0,  
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