anonymous
  • anonymous
Determine the intervals on which the given function is concave up or down and find points of inflection f(x)= (x^2-6)e^x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
need to take the 2nd derivative first f'(x)=(x^2-6)e^x+2xe^x f''(x)=(x^2-6)e^x+2xe^x+2e^x+2xe^x f''(x)=e^x[x^2-6+4x+2] f''(x)=e^x[x^2+4x-4]
anonymous
  • anonymous
now set f''(x)=0 e^x[x^2+4x-4]=0 e^x is never 0, so we'll concern ourselves with x^2+4x-4=0 using the quadratic formula, i got \[x=-2-2\sqrt{2}, -2+2\sqrt{2}\] this splits the domain into three intervals \[(-\infty, -2-2\sqrt{2}), (-2-2\sqrt{2}, -2+2\sqrt{2}), (-2+2\sqrt{2}, \infty)\]
anonymous
  • anonymous
can you find the solutions from here?

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anonymous
  • anonymous
i just needed the intervals ..and if they were concave up or down i couldn't figure out how to find the points after finding the second derivative thank you

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