If the local linear approximation of f(x) = 2cos x + e^2x at x = 2 is used to find the approximation for f(2.1), then the % error of this approximation is?

Answer-

The % error of this approximation is 1.64%

Solution-

Here,

And,

Taking (2, f(2)) as a point and slope as, f'(2), the function would be,

The value of f(2.1) will be

According to given function, f(2.1) will be,

its less than 713.21 but greater than 5.2