Can anyone find all values of x for which the graph of f(x) = (x + 2)(x - 5)^2 is concave downward?

0 ⤊

2006-10-14 05:39:01 · 2 answers · asked by chris 2 in Science & Mathematics ➔ Mathematics

x < 8/3, since it was established in a previous question that it's concave upward for x > 8/3.

2006-10-14 05:55:51 · answer #1 · answered by James L 5 · 0⤊ 0⤋

f(x)=(x+2)(x-5)^2
f ‘ (x)=(x-5)^2 +2(x-5)(x+2)
f “(x)=2(x-5)+2(x+2+x-5) Then: 3x-8=0
x=8/3
If x<(8/3) Then the graph is concave downward

2006-10-14 13:04:05 · answer #2 · answered by matchstick man 1 · 0⤊ 0⤋