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**Some_One** Sketch the graph of a function $\displaystyle f$ that satisfies the following conditions:

.(a) $\displaystyle f(0) = 0$

.(b) $\displaystyle f''(x) > 0$, . $\displaystyle x \neq 0$

.(c) $\displaystyle \mathop {\lim }\limits_{x \to 0^-} f'(x) = \infty$

.(c) $\displaystyle \mathop {\lim }\limits_{x \to 0^+} f'(x) = -\infty$

.(d) $\displaystyle \mathop {\lim }\limits_{x \to -\infty} f(x) = -\infty$

.(d) $\displaystyle \mathop {\lim }\limits_{x \to \infty} f(x) = \infty$

**Interpret each piece of information.**

.

My interpretations are as follows:

.(a) y-intersect at (0,0)

.(b) Concave up for all values of $\displaystyle x$, except at $\displaystyle x = 0$ (possibly an asymptote there?)

.(c) As you approach 0 from the left, the slope approaches infinity and so the function gets higher.

.(c) As you approach 0 from the right, the slope approaches negative infinity and so the function gets lower.

.(d) As you approach negative infinity (left), the function gets lower and lower,

.(d) As you approach positive infinity (right), the function gets higher and higher.

I'm not to sure about them though, and it seems like (b) and (c) are contradictory (if C is true, that would mean concave down to the right of 0)

I would really appreciate a second opinion.