Trapezoidal Rule: Maximum error in approximation?

[Jess Karakov]

Homework Statement

Suppose that T4 is used to approximate the ∫ from 0 to 3 of f(x)dx, where -2 ≤ f ''(x) ≤ 1 for all x. What is the maximum error in the approximation?

Homework Equations

|ET|≤ (K(b-a)^3)/(12n^2)

The Attempt at a Solution

So I know how to find the error of the trapezoidal rule using the above equation, but I do not understand how to find the maximum error in an approximation.
To find the max error I would find the max/mins of f ''(x), right? But I don't know how to do that when f(x) is not given

 

[Ray Vickson]

Homework Statement

Suppose that T4 is used to approximate the ∫ from 0 to 3 of f(x)dx, where -2 ≤ f ''(x) ≤ 1 for all x. What is the maximum error in the approximation?

Homework Equations

|ET|≤ (K(b-a)^3)/(12n^2)

The Attempt at a Solution

So I know how to find the error of the trapezoidal rule using the above equation, but I do not understand how to find the maximum error in an approximation.
To find the max error I would find the max/mins of f ''(x), right? But I don't know how to do that when f(x) is not given

You can't. All you can do is find an upper bound on the absolute error, so your actual error may be a lot less than your bound. Just find an upper bound on $|f''(x)|$ over $x \in [0,3]$.

Note: people hardly ever find best bounds by finding actual maxima of things like $|f''(x)|$; typically, they are satisfied with decent bounds.

 

[Jess Karakov]

So K would just be 2?

 

[Ray Vickson]

So K would just be 2?

You tell me.

 

[Jess Karakov]

yes...