Let f be a function defined for all x >0 such that f(5) =2 and the derivative of f is given by f' (x) = 22-10z+16 for all x >0. a). Find all values of x for which the graph of f has a relative (local) maximum and relative (local) minimum. Be sure to specify which value is the relative maximum and which is the relative minimum. b). Find the minimum value of the slope of f (them minimum value of the derivative, f (x) if x >0. c). Identify any interval(s) over which f is concave up if x >0.
Let f be a function defined for all x >0 such that f(5) =2 and the derivative of f is given by f' (x) = 22-10z+16 for all x >0. a). Find all values of x for which the graph of f has a relative (local) maximum and relative (local) minimum. Be sure to specify which value is the relative maximum and which is the relative minimum. b). Find the minimum value of the slope of f (them minimum value of the derivative, f (x) if x >0. c). Identify any interval(s) over which f is concave up if x >0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let f be a function defined for all x >0 such that f(5) = 2 and the derivative of f is given by
22-10r+16
f' (æ) =
for all x >0.
a). Find all values of x for which the graph of f has a relative (local) maximum and relative (local) minimum. Be sure to specify which value is the relative
maximum and which is the relative minimum.
b). Find the minimum value of the slope of f (them minimum value of the derivative, f'(x) if x >0.
c). Identify any interval(s) over which f is concave up if x >0.
Let g be a function that is continuous on the closed interval [0, 31. The function g and its derivatives are shown in the table below.
0<x<1
1
1<x<2
2
2<x<3
Negative
Negative
Negative
g(x)
1
Positive
-1
Negative
g'(x)
Undefined
Negative
Undefined
Positive
g"(x)
Undefined
Positive
Undefined
Negative
d). Sketch a possible graph of g on a coordinate plane. Upload a picture of it.
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