Suppose f is continuous everywhere, f’ is differentiable everywhere except at x = -1, and the graph of y = f’(x) is in the photo attached. Explain why there exists c ∈ (3, 4) such that f” (c) = -1. Provide a brief justification for your answer.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter5: A Survey Of Other Common Functions
Section5.4: Combining And Decomposing Functions
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Suppose f is continuous everywhere, f’ is differentiable everywhere except at x = -1, and the graph of y = f’(x) is in the photo attached. Explain why there exists c ∈ (3, 4) such that f” (c) = -1. Provide a brief justification for your answer.
Y
4+
3+
2.
1.
-3
(1,0) 2
3
(-3,0)
V
(0, -0.5)
(2,-0.5)
-2-
(3,-2)
-1,-2)
-3+
(-1.-3)
(4, -3)
+
y = f'(x)
I
Transcribed Image Text:Y 4+ 3+ 2. 1. -3 (1,0) 2 3 (-3,0) V (0, -0.5) (2,-0.5) -2- (3,-2) -1,-2) -3+ (-1.-3) (4, -3) + y = f'(x) I
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