A polynomial p(x) has a relative maximum at ( -2,4), a relative minimum at (1,1), a
relative maximum at (5, 7), and no other critical points. How many real zeros does p(x)
have?

Question

A polynomial p(x) has a relative maximum at ( -2,4), a relative minimum at (1,1), a 
relative maximum at (5, 7), and no other critical points. How many real zeros does p(x)
have?

cwrw238 · Answer

the derivative will hve  3 real zeros  so will be cubic
so the polynimial p(x) will have 4 real zeros

anonymous · Answer

how do you know that? I'm very confused. I tried sketching the graph but it does not give me any help.

cwrw238 · Answer

the cubic equation has 3 real zeros because there are 3 critical points
the original function is quartic ( in x^4) so wil  have 4 real zeros