How to show exponential curve is concave up? (1 Viewer)

[enigma_1]

For the curve, y=x - e^x

How do I show that it is concave up?

 

[braintic]

For the curve, y=x - e^x

How do I show that it is concave up?

This curve is concave DOWN.

 

[enigma_1]

Ahh sorry yeah it's mean to be down. How do I show this?

 

[QZP]

Ahh sorry yeah it's mean to be down. How do I show this?

A curve y is concave up if y" > 0, and concave down if y " < 0

 

[enigma_1]

How the hell do u sketch this? I know max pt is at zero, minus 1

 

[lochieferrier]

y' = 1 - e^x
y'' = -e^x
Which is always negative as e^x is always positive. This means the curve is concave down for all real values of x.