# Calculus

the local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangency,

f'(x) <0
f'(x)>0
f"(x) <0
f"(x) >0

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1. the line must lie above the curve, so the graph must be concave down.
So, what do you think?

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2. f"(x) < 0 ???????

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3. right

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4. but I posted this answer in my homework and the teacher marked (zero). I don't know what happened

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5. I can not imagine what happened but agree that the second derivative is negative.

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