8. Iff and g are differentiable at xo such that f(xo) g(xo), prove that each of the functions h = min (f.g) and H= max(f.g) are differentiable at xo. Discuss also the case f(x) = g(xo).
8. Iff and g are differentiable at xo such that f(xo) g(xo), prove that each of the functions h = min (f.g) and H= max(f.g) are differentiable at xo. Discuss also the case f(x) = g(xo).
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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l need the answer in 30 mints please please please.
![8. If f and g are differentiable at x, such that f(x) = g(xo), prove that each of the functions
h = min (f.g) and H = max(f.g}
are differentiable at xo. Discuss also the case f(x) = g(xo).
9. Let (x) and (yn) be two sequences converges to c with x y for all n. Assume that fis
defined for all real numbers and that f'(e) exists. Prove that
[[02-1(²)]
converges to f'(c).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb54994fc-705c-412a-af97-441a93ad8547%2F08cf09fd-bdb2-4f74-ac30-3233ee4a7f32%2Fb5ke4gl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8. If f and g are differentiable at x, such that f(x) = g(xo), prove that each of the functions
h = min (f.g) and H = max(f.g}
are differentiable at xo. Discuss also the case f(x) = g(xo).
9. Let (x) and (yn) be two sequences converges to c with x y for all n. Assume that fis
defined for all real numbers and that f'(e) exists. Prove that
[[02-1(²)]
converges to f'(c).
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