MAT-1110 Midterm: MATH 1110 App State Fall2017 Test3 answer key
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Note that f (x) = 3x4 4x3 = 3x3(cid:18)x . [f (x) is graphed to the right = ] f (x) = 3x3(cid:18)x . 4: make a number line and mark where f (x) is increasing and decreasing. Then x = 4/3 is an oddly repeated root, so f (x) switches to negative. Finally, x = 0 is also oddly repeated, so f (x) becomes positive again. 3: classify each of the critical points of f (x) (i. e. relative min, max, both, or neither). f (x) switches from increasing to decreasing at x = 0, so x = 0 is a local maximum . On the other hand, f (x) is decreasing before x = 4/3 and then is increasing after x = 4/3. Alternatively, we could compute f (x) = 12x3 12x2 and see that f (4/3) = 64/9 > 0 so that x = 4/3 is a local minimum (by the second derivative test).
