I need tips for Math (1 Viewer)

[excellence1]

Is there any clear way or easy way to answer question that ask how to draw an f(x) graph to an f'(x) graph.Any tips are greatly appreciated

 

[excellence1]

“ The graph f(x) has a stationary point when x=1, a point of inflexion when x=3 and a horizontal asymptote y=2. Sketch the graph y=f'X indicating its features at x=1 and at x=3, amd the shape of the graph as x approaches infinity ”

 

[KingOfActing]

Is there any clear way or easy way to answer question that ask how to draw an f(x) graph to an f'(x) graph.Any tips are greatly appreciated

If you're given f(x) then the graph of f'(x) will be 0 at the stationary points, and stationary at the points of inflexion. It'll also be >0 when f(x) is increasing and <0 when f(x) is decreasing.

“ The graph f(x) has a stationary point when x=1, a point of inflexion when x=3 and a horizontal asymptote y=2. Sketch the graph y=f'X indicating its features at x=1 and at x=3, amd the shape of the graph as x approaches infinity ”

What this is telling you is f'(1) = 0, (3,f'(3)) is a stationary point, and as x-> infinity, f'(x) -> 0.

 

[excellence1]

How is the line increasing, isnt it decreasing at 3