Intermediate Value Theorem

tiewkj

Use the Intermediate Value Theorem to show that x^3-7x^2+14x-8=0 has at least one solution in the interval [0,5].Sketch the graph of y=x^3-7x^2+14x-8 over [0,5].How many solutions does this equation really have?

有谁可以教教我要怎样做？

puangenlun

f(x)=x^3-7x^2+14x-8
f(0)<0
f(5)>0
by Intermediate Value Theorem
f(x) has root(s) in the interval [0,5]

f(x) = (x-4) (x-2) (x-1)
so 3 roots