Where is the function {eq}f(x) = |x| {/eq} differentiable?
Question:
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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View this answer{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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What It Means To Be 'Differentiable'
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Chapter 7 / Lesson 7
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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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