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Determine whether f' (0) exists You'll get a detailed solution from a subject matter expert when you start free trial F (x)= {x sin⁡ (1/x) if x≠0, 0 if x=0 calculus

SOLVED:Determine whether a quadratic model exists for each set of

Limits and derivatives section 2.7 F (x) = {x sin 1/x if this problem has been solved Derivatives and rates of change problem 59.

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There is a thereom that states let $f$ be defined on $ [a,b]$

If $f$ has a local maximum at a point $x \in (a,b)$ and if $f ' (x)$ exists then $f ' (x) = 0$ i'm curious as to whether or not that theorem is kosher to use For example, if we consider the function g (x) = sin (x), its derivative at x = 0 exists and equals cos (0) = 1 However, in the case of f (x), the oscillation in values of sin (1/x) prevents a clear derivative from being defined at zero. Determine whether or not exists

I think it is yes because the derivative of 0 is just 0 so f'(0) would still exist at 0 Am i correct or no Answer to determine whether f ' (0) exists 6 x sin if x 0 f (x)

Definition of the derivative and using a squeeze theorem

00:01 number fifty nine of the stuart calculus eighth edition section two point seven determine whether at prime a zero exists and f of x is equal to this peaceful dysfunction. To determine whether the derivative f ′(0) exists for the given function F (x) = xsin(1) 0 if x = 0 if x = 0 we first need to check the continuity of the function at x = 0 before we assess its differentiability Check continuity at x = 0

A function is continuous at a point if limx→a f (x) = f (a) Here, we have f (0) = 0 We need to evaluate limx→0 f (x) = limx→0 xsin(x1 ) So the question asks that for each part i use the definition without evaluating the limit (i'm not sure what that means) and then make a table of values to determine if f' (0) exists in each case.

Answer to determine whether f' (0) exists