My ? is on useing the intermediate value thm for polynomial functions. I dont understand how it works. Here is my Problem. If f(x)=x^3-5x^2+7x-9, use the intermediate value theorem for polynomial functions to prove that there is a real number a such that f(a)=100. Help?
f(0)=-9 and f(10)=561
since f is a continuous function it must attain all the numbers between -9 and 561 on the interval [0,10] (by the IVT)
since 100 is between -9 and 561 we know that there exists an a in [0,10] such that f(a)=100