geometrical applications of calculus (1 Viewer)

[blacktown_]

sketch a function with f'(x)>0 for x<2, f'(2)=0 and f'(x)<0 when x>2

so i know what the sketch looks like as seen from the answers, but i do not know why it's like that.
can someone please explain to me how to interpret questions like these? please!
i don't understand these types of questions

please and thankyou

 

[Peeik]

Sine you already know the picture I will just explain the information.

f'(x)>0 for x<2 is telling you that the function is increasing for the domain x<2.
f'(2)=0 is telling you that there is a stationary point at x=2.
f'(x)<0 when x>2 is telling you that the function is decreasing for the domain x>2.

 

[anwar1506]

Since f'(2)=0, there is a stationary point when x=2.

Since f'(x)>0 for x<2, the gradient is positive for any x-value less than 2 (so that it slopes to the right).

Since f'(x)<0 when x>2, the gradient is negative for any x-value greater than 2 (so that is slopes to the left).

Sketching this, you get a parabola with a maximum at x=2.

 

[blacktown_]

omg, i actually understand how to do it now. thankyou Peeik

 

[Peeik]

omg, i actually understand how to do it now. thankyou Peeik

You are welcome!

 

[Capt Rifle]

just draw out all the outcomes and work out their effect

 

[Capt Rifle]

then sketch!