MAC 2311 Midterm: MAC2311 S06 Test 4
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For the function f (x) = (20 3x2)x3 = 20x3 3x5, nd the fol- lowing. (a) the intervals of increase or decrease. (b) the intervals of concavity. (c) the local extrema. Classify each as a maximum or minimum. (d) the in ection points. (e) sketch the graph of y = f (x) For the function f (x) = (2 x)2, nd the following. (a) evaluate the integral. 1 f (x) dx using a limit of riemann sums: lim n . Rn. (b) evaluate the derivative f (a) using f (x) f (a) lim x a x a. Find the length l of the shortest ladder that will reach from the ground to the building, spanning a fence which is six feet high and four feet from the building. building ladder l. Find the area under the curve y = 1 + x3, over the interval 1 x 10. (7) (10 pts. ) lim x (cid:18) x 2 x (cid:19)x.
