Could someone check if this is the correct way to solve this problem.

For what n will the approximation f(x) be accurate to within .0000001 using

, for some between a and b is.

I think for some between a and b means the absolute value of the max between a and b.

From this part on am I suppose to maximize on [0,1] and put that in place of and then solve for n?

If I do that I get

, where 5 is the max of on [0,1]

Solving this for n gives 2886.75 and rounding it to 2887. So n would have to be 2887.