Question

If f'(x) = absolute value of (x-2) , what would teh graph of y=f(x) look like?

Answer 1

this is the graph of the derivative. looks like \(f'(x)=2-x\) for \(x<2\) and \(f'(x)=x-2\) for \(x>2\)
so your original function would look something like
\(f(x)=2x-\frac{x^2}{2}\) for \(x<2\) and \(f(x)=\frac{x^2}{2}-2x\) for \(x>2\)

Answer 2

Did u get f(x) by integrating? if so how do u integrate absolute values

Answer 3

in other words a parabola that faces down, and then a parabola that faces up
we don't know from the derivative where the function actually is, just what the shape is. so it might look like this

Answer 4

get rid of the abosolute values signs and break in to two parts

Answer 5

but i repeat, we don't know where the function is, just what the curve looks like

Answer 6

first it is a parabola that opens down, then it is a parabola that opens up

Answer 7

oh ok i see hpw teh graph works. but say in teh fuure ow wud i integrate a absolute value? is taht possible