Is $f (x) = 1 - e^{3 x}$ $f(x)=1-e^(3x)$ concave or convex at $x = 2$ $x=2$ ?

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Answer 1 · 2015-11-21T18:13:30

Find the second derivative at $x = 2$ $x=2$

If the second derivative is positive , it's concave up . Likewise, if it is negative , it will be concave down .

$f'=-3e^(3x)$

$f''=-9e^(3x)$

$f''(2) <0$ , so it is concave down or convex

Is f(x)=1-e^(3x)f(x)=1−e3xf(x)=1-e^(3x) concave or convex at x=2x=2x=2?