Geometrical appliacation of differentiation (1 Viewer)

[red802]

a) The graph of y=f'(x) is drawn below

View attachment 13054

i)For what values of x would the curve y=f(x) have stationary points, the answer is 1 and 3, is that right
ii)Write down values of x where any points of inflecion on the curve y = f(x) would occur
iii) Draw y=f''(x) (dont have to do it if u dont want to)
iv)Give the values of x for which the curve y=f(x) is concave down
v) Sketch a possible curve y=f(x), which has the properties shown by y=f'(x), given that the curve y=f(x) passes through the points (-2,0) and (0,4)

IF possible, can u explain how u got the answer or show working out.

 

[_ShiFTy_]

i) Since y=f'(x) is drawn, stationary points occur when f'(x)=0, so that would be when x = 0 and 3
ii) There is an inflexion point when x = 1 and a horizontaly point of inflexion when x = 3 (anyone confirm? im rusty at graphs)
iv) y=f(x) is concave down when the gradient changes from positive to negative, so this occurs when x = 0