Unformatted text preview: Problem 3: (20 pts) Let f ( x ) = x 3 + x . Calculate f (2) using the limit deﬁnition of the derivative . Problem 4: (20 pts) Given the function f ( x ) = ± x 2 + x + 1 if x ≥ 1 3x if x < 1 (a) State the domain of the function. (b) Determine lim x → 1f ( x ). (c) Determine lim x → 1 + f ( x ). (d) Is f ( x ) continuous on its domain? Explain your answer. Problem 5: (20 pts) Let f ( x ) = 3 x 23 x 24 . a) What are the zeros of f ( x )? b) Find all asymptotes for f ( x ). c) Made a careful graph of y = f ( x ). Be sure to label the axes, label the zeros and indicate all asymptotes. Problem 6: (10 pts) Suppose that f (2) =5 and f (2) = 3. Write the formula for the tangent line to f at x = 2. Return this copy of the exam with your solutions....
View
Full Document
 Spring '08
 TAN
 Math, Calculus, Derivative, pts, Convex function

Click to edit the document details