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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.
 Spring '08
 CLARK,C.W./HOY,R.R

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