# Calculus

f(x)=[3x^13]e^(−7x)

On which intervals is the function concave up and concave down?

I know when you find the 2nd derivative, the x-values are 0, 1.34206, and 2.37222, and that the 2nd derivative > 0 at x=1.34205 and < 0 at 2.37222.

How does this tell me the intervals where it's concave up and down?

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1. concave down where f" < 0

better review your text, where it is surely explained and illustrated.

f" < 0 means that the slope is decreasing. So, f is either rising either rising more slowly or falling more quickly. Consider a parabola which opens downward.

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posted by Steve
2. so would concave up be (1.34205, 2.37222)?

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posted by Ann
3. Judging from the graph at

http://www.wolframalpha.com/input/?i=[3x^13]e^%28%E2%88%927x%29+for+x%3D0..3

I'd say it is concave down in that interval. In fact, since

f"(x) = 3x^11 e^-7x (49x^2-182x+156)

if the roots are where you say they are, then since the quadratic factor is a parabola which opens up, it is negative between the roots, meaning that f(x) is indeed concave down in that interval.

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posted by Steve
4. it still says I'm wrong, but thanks for trying

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posted by Ann

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