70. If f has a local minimum value at c, show that the function g(x) -f(x) has a local maximum value at c. 71. Prove Fermat's Theorem for the case in which f has a local minimum at c. 72. A cubic function is a polynomial of degree 3; that is, it has the form f(x) = ax' + bx² + cx + d, where a 0. (a) Show that a cubic function can have two, one, or no critical number(s). Give examples and sketches to illustrate the three possibilities. (b) How many local extreme values can a cubic function have?

70. If f has a local minimum value at c, show that the function g(x) -f(x) has a local maximum value at c. 71. Prove Fermat's Theorem for the case in which f has a local minimum at c. 72. A cubic function is a polynomial of degree 3; that is, it has the form f(x) = ax' + bx² + cx + d, where a 0. (a) Show that a cubic function can have two, one, or no critical number(s). Give examples and sketches to illustrate the three possibilities. (b) How many local extreme values can a cubic function have?

Name: Problem 72 70. If f has a local minimum value at c, show that the func
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Description: Problem 72 70. If f has a local minimum value at c, show that the functiong(x)-f(x) has a local maximum value at c.71. Prove Fermat's Theorem for the case in which f has alocal minimum at c.72. A cubic function is a polynomial of degree 3; that is, i

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 98E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

Problem 72

70. If f has a local minimum value at c, show that the function
g(x)
-f(x) has a local maximum value at c.
71. Prove Fermat's Theorem for the case in which f has a
local minimum at c.
72. A cubic function is a polynomial of degree 3; that is, it has
the form f(x) = ax' + bx² + cx + d, where a 0.
(a) Show that a cubic function can have two, one, or no
critical number(s). Give examples and sketches to
illustrate the three possibilities.
(b) How many local extreme values can a cubic function
have?

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