In each of the following, if there exists a function f whose domain is the entir

Question

In each of the following, if there exists a function f whose domain is the entire real line and that satisfies the given condition, give an example of such a function; otherwise just write Does Not Exist inside the box. No further explanation is required..No partial points will he given. f is continuous at 0 and f is not differentiable at 0. (f(x))^2 is differentiable at x = 0. f'(3) = 5 and lim_x rightarrow 3 f(x) = infinity f(3) = 5 and lim_x rightarrow 3 f'(x) = infinity f is not constant and (f'(x))2 - f(x) is constant.

Explanation / Answer

a) f(x) =|x| is not differentiable at x=0, Answer

(|x|)^2 = x^2 is differentiable at x=0.

b)DOES NOT EXIST

c)DOES NOT EXIST

d) f(x) = x^2/4 Answer

f'(x) =2x/4 = x/2
(f'(x))^2 -f(x) = x^2/4 - x^2/4 = 0 Constant

e)DOES NOT EXIST

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