Derivatives with maximum and tendencies

Question

anonymous · Answer

What about them?

lukecrayonz · Answer

http://gyazo.com/173d88962f93e3d4f8d764a9173538b1

lukecrayonz · Answer

sorry I meant limits tendencies and critical points

anonymous · Answer

Do you differentiate using the limit approach or the power rule?

lukecrayonz · Answer

Power rule

anonymous · Answer

ok give me a minute ill explain this

anonymous · Answer

Ok i'm fairly sure about this.

First take the derivate of e^(x/9) and get (e^(x/9))/9 = f'(x)
Putting f'(x) = 0 does not give us any values for x and the function can not be undefined by any means of x. This means there are no critical points. 
Also, since the function f'(x) is always positive for all x-values it is always rising. 

The second derivative f''(x) is also positive for all x values, meaning it is concave up everywhere inside the interval. Putting f''(x) = 0 also yields no values so there are no inflection points.

I believe the answer is C.

lukecrayonz · Answer

Oh okay! I didn't know critical points were just derivative f(x)=0

lukecrayonz · Answer

Thank you so much :-)

anonymous · Answer

No problem :)