Sketch a possible graph of a continuous function f that has domain [-3, 3], where f(-1) = 1 and the graph of y = f'(x) is shown below

Question

zubhanwc3 · Answer

attachment

anonymous · Answer

graph something that looks sort of like $-x^2$ and then graph something that looks similar to $x^3$

zubhanwc3 · Answer

this -x^2 is to the left,and the x^3 is to the right?

jim_thompson5910 · Answer

|dw:1411955276897:dw|

jim_thompson5910 · Answer

plot the point (-1,1) since we know f(-1) = 1

|dw:1411955331843:dw|

jim_thompson5910 · Answer

according to the graph of f ' (x), the straight line on the left piece goes through (-1,0)

because f ' (x) changes from positive to negative through this root, we know there is a local max at x = -1, so there is a local max at (-1,1)

we might have something like this upside down parabola

|dw:1411955405038:dw|

it starts at x = -3 since this is the left edge of the domain and stops at x = 1 because this is where the left straight line piece stops (in f ' (x) )