Question

Sketch the graph of a function f for which f(0) = -1, f '(0)=0, f '(x) < 0 if x < 0, and f '(x) > 0 if x > 0

Answer 1

start with what you know
f(0) = -1 means there is a y-intercept at y=-1
f'(0) =0 means the slope is zero and there is a max or min at x=0
f'(x) <0 means function is decreasing
f'(x) >0 means function is increasing

Answer 2

Oh, I see. I am more confused on how I would sketch a graph with no slope.

Answer 3

Oh wait, is it a horizontal line?

Answer 4

yes, zero slope just means the tangent line is horizontal

Answer 5

herp derp lol. I think the notation just throws me off.
Well, thanks for clarifying! :)

Answer 6

yw
so when you graph this, pick a point x<0 ... and go down because f is decreasing, then stop at (0,-1) and start going up because now f is increasing

what does it look like?

Answer 7

I just put a point on (0,-1) and drew a horizontal line across it.

Answer 8

Is that right?

Answer 9

no because that means function is constant but you it to be decreasing for x<0 and increasing for x>0

Answer 10

I thought the slope was 0

Answer 11

let me draw it out i guess so you can see what i mean