Proving differentiability for a function from the definition

member 731016
Homework Statement
Please see below
Relevant Equations
Please see below
For this problem,
1715475811269.png

The solution is,
1715475847832.png

However, does someone please know why we allowed to assume that the derivative exists for f i.e ##f'(a) = \lim_{x \to a} \frac{f(x) - f(a)}{x - a}##?

Thanks!
 
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ChiralSuperfields said:
Homework Statement: Please see below
Relevant Equations: Please see below

For this problem,
View attachment 345049
The solution is,
View attachment 345050
However, does someone please know why we allowed to assume that the derivative exists for f i.e ##f'(a) = \lim_{x \to a} \frac{f(x) - f(a)}{x - a}##?

Thanks!
Because of the first sentence: Let ##f## be a differentiable function.
 
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