For the function f(x)=(x^(2)+4x+(11/4)e^(x) I need to find where it is concave up.
So, I found the first derivative and then the second derivative which is,
f''(x)= e^(x)(x^(2)+8x+(51/4))
Then, I found the roots of the function using the quadratic formula which is (-8+/-sqrt(13))/(2)
I found it was concave upwards at the open interval: (((-8+sqrt(13))/2), inf)
But somehow this is incorrect. Can someone help me?