If f(x)=x^3-5x^2+7x-9, use IVT for poly fcns to prove that

[Stranger_1973]

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?

[Martingale]

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

[Stranger_1973]

So I can use f(6)=69 and f(7)=138 to say that f(a)=100 for 6<a<7?

[Martingale]

So I can use f(6)=69 and f(7)=138 to say that f(a)=100 for 6<a<7?

yes

[Martingale]

you could also use f(6.5)=99.875 and f(6.51)=100.563951

so

[Stranger_1973]

thanks!