# Exam2_3 9 - (iii) is decreasing when f ′ < 0, (iv) has...

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Version 208 – Exam 2 – Radin – (58305) 9 One is the graph of a function f , one is its derivative f , and one is its second derivative f ′′ . Identify which graph goes with which function. 1. f : f : f ′′ : 2. f : f : f ′′ : 3. f : f : f ′′ : correct 4. f : f : f ′′ : 5. f : f : f ′′ : 6. f : f : f ′′ : Explanation: Calculus tells us that f (i) has horizontal tangent at ( x 0 , f ( x 0 )) when f crosses the x -axis, (ii) is increasing when f > 0, and
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Unformatted text preview: (iii) is decreasing when f ′ < 0, (iv) has a local max at x when f ′ ( x ) = 0 and f ′′ ( x ) < 0, (v) has a local min at x when f ′ ( x ) = 0 and f ′′ ( x ) > 0, (vi) is concave up when f ′′ > 0, (v) and concave down when f ′′ < 0. Inspection of the graphs thus shows that f : f ′ : f ′′ : ....
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## This note was uploaded on 02/14/2012 for the course MATH 408 K taught by Professor Clark,c.w./hoy,r.r during the Spring '08 term at University of Texas at Austin.

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