MATH 1350 Midterm: Math135SolExam2Math135
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The exam has 7 problems on 3 pages! To get full credit, you must show all work: problem 1, find the derivative of the following functions" (a) f(x) = esm 3x, f"(x) = . e. ~~("x) l-v"i (" x) . (b) g(x) = in(2x + 1), g"(x) = ~. Find the equation of the tangent line to the curve at the point where :r = 1. y= x2ex-1. ;\1: problem 3 (a) find the derivative of the function f(x) = x ":j 07" (b) determine the points (if any) where the tangent line to the graph y = f(x) is horizontal. "2. xj ( x + \) (i - x) z rx. ( x. +i)~ Using implicit differentiation, find ~, given that x2 + 2y2 = 3. 4y: problem 5 (a) find the linear approximation (b) write down the differential dy, where y = vi + 3x. of f(x) = /f+3x near x = o. (0. )
