Question

Please help me find the concave up and down for this equation. I already got of the other answers, did the derivative and all, but just the concave up and down i don't quite understand

here; ƒ(x)=(9-4x)e^x

Answer 1

need the second derivative right?

Answer 2

i get \((1-4x)e^x\)
since \(e^x\) is always positive, it comes down to solving \(1-4x>0\) for concave up

Answer 3

function is concave up is second derivative is positive, concave down is second derivative is negative. so step one for solving a concavity problem is finding the second derivative, step two is figuring out where it is positive and negative.
in the example it is positive if \[1-4x>0\] i.e.
\[x<\frac{1}{4}\] and so it is concave up on \((-\infty, \frac{1}{4})\) and concave down on \((\frac{1}{4},\infty)\)

Answer 4

thanks satellite73!