Question

At what numbers is the following function $g$ differentiable? $$ g(x)= \begin{cases}2 x & \text { if } x \leqslant 0 \\ 2 x-x^2 & \text { if } 0<x<2 \\ 2-x & \text { if } x \geqslant 2\end{cases} $$ Give a formula for $g^{\prime}$ and sketch the graphs of $g$ and $g^{\prime}$.

Name: Problem 76, Chapter 3: Single Variable Calculus: Early Transcendentals
Uploaded: 2020-10-16T14:08:17-08:00
Duration: 3 min 45 s
Channel: Jack Gage
Description: At what numbers is the following function g differentiable? g(x)= 2 x if x ⩽0 2 x-x^2 if 0<x<2 2-x if x ⩾2 Give a formula for g^' and sketch the graphs of g and g^'.

   At what numbers is the following function $g$ differentiable?

$$
g(x)= \begin{cases}2 x & \text { if } x \leqslant 0 \\ 2 x-x^2 & \text { if } 0<x<2 \\ 2-x & \text { if } x \geqslant 2\end{cases}
$$


Give a formula for $g^{\prime}$ and sketch the graphs of $g$ and $g^{\prime}$.

Single Variable Calculus: Early Transcendentals

James Stewart,… 9th Edition

Chapter 3, Problem 76

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At what numbers is the following function $g$ differentiable? $$ g(x)= \begin{cases}2 x & \text { if } x \leqslant 0 \\ 2 x-x^2 & \text { if } 0<x<2 \\ 2-x & \text { if } x \geqslant 2\end{cases} $$ Give a formula for $g^{\prime}$ and sketch the graphs of $g$ and $g^{\prime}$.