which conclusion(s) can be made if you know the following? Justify your conclusion(s)

[lovetolearn]

which conclusion(s) can be made if you know the following? Justify your conclusion(s)

a. f'(c)=0, f(c) exists, f'(c-∆x)<0 and f'(c+∆x)>0
b. f(-1) exists, f'(-1)>0, and f''(-1)<0

a. I put an inflection slope=0 function increases in one direction and decreases in the other.
b. I put increasing with x but rate of increase is decreasing.

 

[wjm11]

which conclusion(s) can be made if you know the following? Justify your conclusion(s)

a. f'(c)=0, f(c) exists, f'(c-∆x)<0 and f'(c+∆x)>0
b. f(-1) exists, f'(-1)>0, and f''(-1)<0

a. I put an inflection slope=0 function increases in one direction and decreases in the other.
b. I put increasing with x but rate of increase is decreasing.

You're on the right track. You just need to be a bit more clear/explicit.

a. local minimum (Try drawing a sketch to help see this. Make a point and draw a short, horizontal line through it. Next, add a short, negative slope line to the left of it and a short, positive slope line on the right. Combine these together to make an upwards opening parabola (sort of)).

b. positive slope; concave downward

 

[lovetolearn]

Thank you so much!

 

[HallsofIvy]

which conclusion(s) can be made if you know the following? Justify your conclusion(s)

a. f'(c)=0, f(c) exists, f'(c-∆x)<0 and f'(c+∆x)>0
b. f(-1) exists, f'(-1)>0, and f''(-1)<0

a. I put an inflection slope=0 function increases in one direction and decreases in the other.
b. I put increasing with x but rate of increase is decreasing.

We can't really know anything without a clearer statement of the question! Apparently you intend that [itex]\Delta x[/itex] is a small positive numbre- but you have to say that!