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1024worksheet5

# 1024worksheet5 - f x(b On what interval(s is f x positive(c...

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Polytechnic Institute of NYU MA 1024/1324 Worksheet 5 Print Name: Signature: ID #: Instructor/Section: Directions: Show all your work for every problem. Problem Possible Points 1 10 2 10 3 10 4 15 5 15 6 10 7 10 8 10 9 10 Total 100 1

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2 (1) Given the graph of f ( x ). Sketch the graph of f 0 ( x ) on the second set of coordinates.
3 (2) Find a formula for the derivative of the functions using the limit deﬁnition of the derivative. (a) f ( x ) = 5 x - x 2 (b) f ( x ) = 1 x + 3

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4 (3) Find A and B given that the function f ( x ) = ± x 3 , x 1 Ax + B, x > 1 is diﬀerentiable at x = 1.
5 (4) Let f ( x ) = ± ( x + 1) 2 , x 0 ( x - 1) 2 , x > 0 (a) Compute f 0 ( x ) for x 6 = 0. (b) Show that f is not diﬀerentiable at x = 0.

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6 (5) The graph of f 0 ( x ) is given: At which of the marked values of x is: (a) f ( x ) greatest? (b) f 0 ( x ) greatest? (c) f 00 ( x ) greatest? (d) f ( x ) least? (e) f 0 ( x ) least? (f) f 00 ( x ) least?
7 (6) Give the signs of f , f 0 , f 00 at each point. (a) x = - 2 . 5 (b) x = - 1 . 5 (c) x = . 5 (d) x = 1 . 5

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8 (7) Given f ( x ): (a) What are the critical points of

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Unformatted text preview: f ( x )? (b) On what interval(s) is f ( x ) positive? (c) On what interval(s) is f 00 ( x ) negative? (d) What are the inﬂection point(s)? 9 (8) (a) Sketch a graph of a continuous function that whose ﬁrst derivative is positive everywhere, second derivative is negative everywhere, f (1) = 1, and f (1) = . 25. (b) Sketch a graph of a continuous function that whose ﬁrst derivative is negative everywhere, second derivative is positive everywhere, f (-2) = 1, and f (-2) =-2. 10 (9) Given the graph of g ( x ). (a) What are the critical points of g ( x )? (b) Sketch the graph of g ( x ) on the given set of coordinates....
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1024worksheet5 - f x(b On what interval(s is f x positive(c...

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