Where is the function {eq}f(x) = |x| {/eq} differentiable?


Where is the function {eq}f(x) = |x| {/eq} differentiable?

Differentiability of a Function:

A function {eq}f:\mathbb{R} \rightarrow \mathbb{R} {/eq} is said to be differentiable at a point {eq}a {/eq} if {eq}\lim_{h\rightarrow 0}\frac{f(a+h)-f(a)}{h} {/eq} exists and it is said to be the derivative of the function at a point {eq}a {/eq} and it is denoted by {eq}f^{\prime}(a) {/eq}.

Answer and Explanation: 1

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{eq}f(x)=|x| {/eq}.
If {eq}x>0 {/eq} then {eq}f(x)=x \Rightarrow f^{\prime}(x)=\lim_{h\rightarrow 0}\frac{(x+h)-x}{h}= \lim_{h\rightarrow...

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Learn more about this topic:

What It Means To Be 'Differentiable'


Chapter 7 / Lesson 7

Learn about differentiability. Understand how to tell if a function is differentiable and when it isn't and see a comparison of differentiable vs. continuous.

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