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Problem 2: For the following statements, say whether they are true or false. If true, provide a brief explanation. If false, provide a counterexample. (bASuppose: f(x+h)- f(a) = L lim h- 0 h2 Then f'(x) 0. (d) Suppose that f and g are two continuously differentiable functions such that f' (0) < g'(0) and f'(1)> g' (1). Then f(x) - g(x) has a local maximum somewhere on (0, 1). (e) If f is increasing on (0,2) and decreasing on (1, 3), then f is differentiable on (1, 2)

Problem 2: For the following statements, say whether they are true or false. If true, provide a brief explanation. If false, provide a counterexample. (bASuppose: f(x+h)- f(a) = L lim h- 0 h2 Then f'(x) 0. (d) Suppose that f and g are two continuously differentiable functions such that f' (0) < g'(0) and f'(1)> g' (1). Then f(x) - g(x) has a local maximum somewhere on (0, 1). (e) If f is increasing on (0,2) and decreasing on (1, 3), then f is differentiable on (1, 2)

Advanced Engineering Mathematics
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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Problem 2: For the following statements, say whether they are true or false. If true, provide a brief explanation. If false, provide a counterexample. (bASuppose: f(x+h)- f(a) = L lim h- 0 h2 Then f'(x) 0. (d) Suppose that f and g are two continuously differentiable functions such that f' (0) < g'(0) and f'(1)> g' (1). Then f(x) - g(x) has a local maximum somewhere on (0, 1). (e) If f is increasing on (0,2) and decreasing on (1, 3), then f is differentiable on (1, 2)
Transcribed Image Text:Problem 2: For the following statements, say whether they are true or false. If true, provide a brief explanation. If false, provide a counterexample. (bASuppose: f(x+h)- f(a) = L lim h- 0 h2 Then f'(x) 0. (d) Suppose that f and g are two continuously differentiable functions such that f' (0) < g'(0) and f'(1)> g' (1). Then f(x) - g(x) has a local maximum somewhere on (0, 1). (e) If f is increasing on (0,2) and decreasing on (1, 3), then f is differentiable on (1, 2)
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