Consider the function f(x)=-x^2 for x \leq 1 and f(x)=x^3 for x>1 . Which of the following are True?

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Consider the function f(x)=-x^2 for $x \leq 1$ x \leq 1 and f(x)=x^3 for x>1. Which of the following are True?

$\lim_{x\to 1^-} f'(x)=-2$ \lim_{x\to 1^-} f'(x)=-2

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$\lim_{x\to 1^+} f(x)=1$ \lim_{x\to 1^+} f(x)=1

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f is right continuous at 1.

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$\lim_{x\to 1^+} f'(x)=3$ \lim_{x\to 1^+} f'(x)=3

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$\lim_{x\to 1^-} f(x)=(-1)^+$ \lim_{x\to 1^-} f(x)=(-1)^+

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$\lim_{x\to 1^+} f(x)=1^+$ \lim_{x\to 1^+} f(x)=1^+

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$\lim_{x\to 1^-} f'(x)=(-2)^-$ \lim_{x\to 1^-} f'(x)=(-2)^-

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f is left continuous at 1.

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$\lim_{x\to 1} f(x)$ \lim_{x\to 1} f(x) does not exist

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f is right differentiable at 1 with $f'_{+}(1)=3$ f'_{+}(1)=3

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f is left differentiable at 1 with $f'_{-}(1)=-2$ f'_{-}(1)=-2

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f is differentiable at 1

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f is continuous at 1.

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