Intermediate Value Theorem & F(x)=(x-7)(x-8)+ x^2: Find a<c<b proving F(c)=53

[moonbloe]

Intermediate Value Theorem & F(x)=(x-7)(x-8)+ x^2: Find a<c<b proving F(c)=53

Consider the function F(x)=(x-7)(x-8)+ x². Use the Intermediate Value Theorem with a decent interval [a,b] to demonstrate that a value c exists so that F(c)=53. Write the interval [a,b] used. Explain.

I have a huge interval resulting from this problem and I want to know the answer,

 

[Deleted member 4993]

Consider the function F(x)=(x-7)(x-8)+ x². Use the Intermediate Value Theorem with a decent interval [a,b] to demonstrate that a value c exists so that F(c)=53. Write the interval [a,b] used. Explain.

I have a huge interval resulting from this problem and I want to know the answer,

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/for

 

[Steven G]

Consider the function F(x)=(x-7)(x-8)+ x². Use the Intermediate Value Theorem with a decent interval [a,b] to demonstrate that a value c exists so that F(c)=53. Write the interval [a,b] used. Explain.

I have a huge interval resulting from this problem and I want to know the answer,

Even if we were to do this problem for you, we can't because you did not give us this big interval you speak of. Why not?

Does the IVT say that the interval [a,b] must be small?