This problem investigates the derivative of the absolute value function. Recall that we define the absolute value as:|x|={xif x≥0−xif x&lt;0a) In the space provided, draw a graph of the function f(x)=|x|b) Using your draph from part (a), and your understanding of the derivative as the rate of change/slope of the tangent line, find the derivative function f′(x) of the above function f(x)=|x|, for x not equal to 0 (fill in the bla):f′(x)={if x&gt;0if x&lt;0c) But what about f′(0)? It is not so clear from the picture even how to draw a tangent line to the function at the origin. So let's try to compute f′(0) by first looking at the corresponding lefthand and righthand limits of the difference quotient.i. Compute limh→0+f(0+h)−f(0)h. Hint: use the piecewise definition of f(x) given above.ii. Compute limh→0−f(0+h)−f(0)hiii. What do your answers to parts (i) and (ii) tell you about f′(0)? Please explain.

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This problem investigates the derivative of the absolute value function. Recall that we define the absolute value as:|x|={xif x≥0−xif x&amp;lt;0a) In the space provided, draw a graph of the function f(x)=|x|b) Using your draph from part (a), and your understanding of the derivative as the rate of change/slope of the tangent line, find the derivative function f′(x) of the above function f(x)=|x|, for x not equal to 0 (fill in the bla):f′(x)={if x&amp;gt;0if x&amp;lt;0c) But what about f′(0)? It is not so clear from the picture even how to draw a tangent line to the function at the origin. So let&#039;s try to compute f′(0) by first looking at the corresponding lefthand and righthand limits of the difference quotient.i. Compute limh→0+f(0+h)−f(0)h. Hint: use the piecewise definition of f(x) given above.ii. Compute limh→0−f(0+h)−f(0)hiii. What do your answers to parts (i) and (ii) tell you about f′(0)? Please explain.

Mary Ramirez · Accepted Answer

Step 1|x|={xif x≥0−xif x&amp;lt;0a) b) f′(x)={1if x&amp;gt;0−1if x&amp;lt;0c) limh→0+f(0+k)−f(0)h=(0+h)−0h=1limh→0−f(⊕h)−f(0)h=limh→0−−(0+h)−0h=−1Since: L⋅H⋅L≠R⋅H⋅LThe function is not differentialli at x=0, but is continous at x=0

This problem investigates the derivative of the absolute value function. Recall

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