6. Find a cubic function f(r) = ar³ + bx² + cx +d that has a local maximum value of 3 at r =-2 and a local minimum value of 0 at r = 1.

College Algebra (MindTap Course List)
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ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
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How do I do number 6

"high-caliber" athletes finishes in a tie. Show that at some point during the race, Sam and Michael
were running at the same speed.
5. A number a is called a fixed point of a function f if f(a) = a. Prove that if f'(r)#1 for all real
numbers r, then f has at most one fixed point.
6. Find a cubic function f(r) = ax + bx? + cr +d that has a local maximum value of 3 at r =-2 and
a local minimum value of 0 at r 1.
7. Sketch the graph of a function f that satisfies the following: f'(0) = f'(2) = f'(4) = 0, f'(x) > 0 if
x < 0 or 2 < x < 4, f'(x) < 0 if 0<x < 2 or a > 4, f"(x) > 0 if 1 < x < 3, and f"(x) < 0 if z<1
or r > 3.
Evaluate the following limits:
8. lim (x VI
(e)
9. lim sin
I +x+5
10. lim
+2+1
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Transcribed Image Text:"high-caliber" athletes finishes in a tie. Show that at some point during the race, Sam and Michael were running at the same speed. 5. A number a is called a fixed point of a function f if f(a) = a. Prove that if f'(r)#1 for all real numbers r, then f has at most one fixed point. 6. Find a cubic function f(r) = ax + bx? + cr +d that has a local maximum value of 3 at r =-2 and a local minimum value of 0 at r 1. 7. Sketch the graph of a function f that satisfies the following: f'(0) = f'(2) = f'(4) = 0, f'(x) > 0 if x < 0 or 2 < x < 4, f'(x) < 0 if 0<x < 2 or a > 4, f"(x) > 0 if 1 < x < 3, and f"(x) < 0 if z<1 or r > 3. Evaluate the following limits: 8. lim (x VI (e) 9. lim sin I +x+5 10. lim +2+1 Download A Print Activity Details
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