G'day, aussiekid90!
Your answers are correct . . .
1. If $\displaystyle f(x)\:=\:x^22x$, is $\displaystyle f(x)$ differentiable at $\displaystyle x=0$? The graph of $\displaystyle f(x) \:=\:x^22x$ looks like this: Code:
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In the graph of $\displaystyle g(x) \:=\:x^22x$,
. . anything below the xaxis is reflected upward. Code:
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The graph has two different slopes at $\displaystyle x = 0$.
. . The function is not differentiable there.
2. For the same curve, is $\displaystyle f(x)$ differentiable at $\displaystyle x=0$?
The graph of $\displaystyle f(x)$ is symmetric to the yaxis.
The graph looks like this: Code:
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The graph has two different slopes at $\displaystyle x=0$.
. . The function is not differentiable there.