The graph of a twice-differentiable function

[Fatima Hasan]

Homework Statement

How to determine the graph using the properties of a twice-differentiable function ?

Homework Equations

None

The Attempt at a Solution

when x < 2 , y ' > 0 . So, the function is increasing on this interval. But , the correct answer is ( D) and the function is decreasing when x < 2.
Could somebody help me to solve this problem ?
Thank you for your help

 

[phyzguy]

The top line in the problem must be an error. To be consistent with the rest of the problem, it should read x < -2.

 

[Ray Vickson]

Homework Statement

How to determine the graph using the properties of a twice-differentiable function ?
View attachment 217909
View attachment 217910

Homework Equations

None

The Attempt at a Solution

when x < 2 , y ' > 0 . So, the function is increasing on this interval. But , the correct answer is ( D) and the function is decreasing when x < 2.
Could somebody help me to solve this problem ?
Thank you for your help

There must be a typographical error in the question: the first line $x < 2 \hspace{2em} y'>0, y''<0$ should read as $x < - 2 \hspace{2em} y'>0, y''<0$.

Can you see why the original printed form (with $x < 2$ instead of $x < -2$) does not make sense?

 

[fresh_42]

There is probably a typo in the first line. I think it should be $x<-2$, because otherwise it would contradict the following conditions. Thus it is increasing left of this point, which excludes A and B. The distinction between C and D is then done by the values at the extremes.