Homework Statement
Let P(x) be any polynomial of degree at least 2, all of whose roots are real and distinct. Prove that all of the roots of P'(x) must be real. What happens if some of the roots of P are multiple roots?
Homework Equations
I think that question is related to the concept...
I realize it is continous. I just need prove that it is continuous using the definition of continuous
for every ε > 0 there exists a δ > 0 such that for all x ∈ I,: |x-c|<δ⇒|f(x)-f(c)|<ε
prove that the equation (1-x)Cosx=Sinx has at least one solution in (0,1)
I am having some problem in proving that the equation is continous.
Please help. Thank you