MATH 211 Midterm: MATH 211 NIU s03Test1Solution
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Solutions: (20 pts; 5 pts each) find the following derivatives, using the formulas we have studied. (a) f (x) = x4 5x3 + 2x + 11. The tangent line is horizontal when the slope is zero, so we need to set y = 0. The points are ( 1, 4) and (1, 0). x = 1. 3x2 = 3 x2 = 1: (10 pts) graph y = The shape is almost the same as y = (there is a graph posted separately on the web. ) , on quiz 1: (15 pts; compare p163 #77) find an equation of the tangent line to the graph of y = (0, 2). Graph the tangent lines on the axes given above. x 1. 2 at the point y = (0)(x 1) (2)(1) Equation of the tangent line: (x 1)2 at (0, 2): y = 2(x 0) 2 at (3, 1): y = 1. = lim x 3 x + 1 x 1.
