Question
Exercise 1: For the following properties, give an example of a functionf that is continuous everywhere and
satisfies the given conditions
|(a) f(x) f(x) for all xE R
(b) f'(1)2, f(1) 7
1 for x < 0, but f'(x)< -1 for
(c) f'(x)
> 0
(d) f is differentiable everywhere with f"(x) > 0 for all r E R, but f"(x) is not differentiable at x = 0
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Transcribed Image Text

Exercise 1: For the following properties, give an example of a functionf that is continuous everywhere and satisfies the given conditions |(a) f(x) f(x) for all xE R (b) f'(1)2, f(1) 7 1 for x < 0, but f'(x)< -1 for (c) f'(x) > 0 (d) f is differentiable everywhere with f"(x) > 0 for all r E R, but f"(x) is not differentiable at x = 0

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