MATH 151 Midterm: MATH 151 TAMU Y2017 2017c X3A Solutions
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This means that f changes from concave down to concave up there. Hence x = 3 is an in ection point of f . Here are the multiple choice answers for version a. Second derivative test: the step size is x = 7 1. Our area estimate is 2 ( f (1) + f (3) + f (5)). Recalling that f (x) = x2 + 1, this gives 2 (2 + 10 + 26) = 2 (38) = 76: now f (x) = 15x4 15x2 = 15x2 (x 1) (x + 1). Therefore f (x) > 0 and hence f is increasing for x < 1 or x > 1. Via l"h, as x(cid:1) = tan(3/x: as x , x tan(cid:0) 3 x2 sec2(cid:0) 3 x , 3 x(cid:1) 2 : via the mvt, we have f (c) = f (3) f (1, the area of a triangle is 1.
