180_Midterm2_sampleA

180_Midterm2_sampleA - 4. Let f ( x ) = x 3-3 x . Give a...

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MATH 180 Sample Midterm exam 1.Find the derivative of the following functions: i) f ( x ) = x 5 ln( x 3 + 1) ii) f ( x ) = sin ( xe x ) + e sin x iii) f ( x ) = arctan(5 x + 3) 2. Consider the function y defined by the equation x 3 y 3 + x 2 + y 2 = 3. Find the tangent at the point (1 , 1) 3. Find the critical points of the function f ( x ) = x 3 +3 x 2 - 4 x +5 and determine if they correspond to local extrema.
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Unformatted text preview: 4. Let f ( x ) = x 3-3 x . Give a table that shows the monotonicity and concavity of f . Then use it to sketch the graph of f 5. Find the minimum and the maximum of the function f ( x ) = e x 2 +1 on the interval [-1 , 1]. 1...
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