Question

let G(x)= e^x(x^2+1)
find the intervals it is concave up
I found the derivative (e^x(x+1)+e^x(2x)) but it's supposed to be -1, -3 as the x values and i can't seem to get that

Answer 1

concave up/down is determined by the second derivative. the answer you gave is only for the first derivative

Answer 2

omg thank you so much!!

Answer 3

when you check for concave up/down do you plug your poi back into the original equation or the second derivative

Answer 4

back into the original function. the point lies on the curve described by the function

Answer 5

if i was looking for the maximum value, would i plug the poi into the original function? how could you find the value without a calculator?

Answer 6

if you want the max/min value, use the first derivative only. the second derivative will confirm IF it is indeed a maximum or a minimum.

Answer 7

as to your first derivative \[\large e^x(x^2+2x+1)=0\]note the e^x>0, so it is the other factor (x^2 + 2x + 1) that has a root, where x = -1 where it is a relative maximum. here's the graph to aid you.