Concavity And The Second Derivative Test Worksheet With Answers Page 7
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9nd
Calculus Maximus
WS 3.4: Concavity & 2
Deriv Test
( )
x ≠
= − and the derivative of h is given by
17. Let h be a function defined for all
0
such that
h
4
3
2
−
x
2
( )
′
=
∀ ≠ .
h x
,
x
0
x
(a) Find all values of x for which the graph of h has a horizontal tangent, and determine whether h has a
local maximum, a local minimum, or neither at each of these values. Justify your answers.
(b) On what intervals, if any, is the graph of h concave up? Justify your answer.
x = .
(c) Write an equation for the tangent to the graph of h at
4
x = lie above or below the graph of h for
x > ? Why?
(d) Does the line tangent to the graph of h at
4
4
≤ ≤ lie above or below the graph of h for on
(e) Does the secant line to the graph of h for 3
x
5
≤ ≤ ? Why?
3
x
5
Page 7 of 9
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