. For which values of h will f have three distinct zeros?
How do I do this too.
I guess they need a height for the graph where you get three roots. If I differentiate the function, I see that y would have to be above the x axis on x = 2, and below the x axis on x = 0.
Sorry, forgot to mention h has to be a constant.
The answers in the book are
(a) all h > 4
(b) 0 < h < 4
(c) all h < 0
(d) -4 < h < 0
(e) all h < -4
I think that I could rule out a,c,e because then at some point in the graph, there will only be one root instead of three.