Finding Inflection Points for y=(^3 +6x^2 +15x +19)e^-x

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Homework Statement


find the inflection points of the curve y=(^3 +6x^2 +15x +19)e^-x correct to five decimal places


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The Attempt at a Solution


i know how to find the inflection points. you graph the derivative and find where the concavity shifts. but the e^-x really throws me off
 
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Steps:
1)take 2 derivatives
2)set result equal to zero
3)solutions are inflection points
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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