Question

How do you tell if the function y= 2x+e^x is increasing/decreasing and concave up/concave down ?

Answer 1

the bigger x is the bigger y is,

Answer 2

f(x) is increasing if f'(x) > 0

f(x) is decreasing if f'(x) < 0

Answer 3

okay then how would you tell if it was concave up/down?

Answer 4

Do you have an interval?

Answer 5

Concave up/down is told by the second derivative. So

f(x) is concave up if f''(x) > 0
f(x) is concave down if f''(x) < 0

Answer 6

oh okay so ill have to take y' and y'' to find inc/dec and concave up/down

Answer 7

but a function could be concave up and down simultaneously depending upon the interval and so is increasing or decreasing.

Answer 8

I dont think i understand what you mean by interval :s

Answer 9

2x is increasing...
e^x is increasing...
2x + e^x increases

2x no concavity
e^x concave up
2x + e^x concave up...

would the teacher accept this instead of the analysis?

Answer 10

If f '(x) is increasing then the function is concave up and if f '(x) is decreasing then the function is concave down.

Answer 11

You may consider reading about inflection points.

Answer 12

thanks for the help everyone, ill try analysing the function by find y' and y''.