The Newton quotient may be used to estimate the first derivative f (x) of a function f (x), if h is ‘small’. Write a program to compute the Newton quotient for the function f (x) = x 2 at the point x...

The Newton quotient

may be used to estimate the first derivative f (x) of a function f (x), if h is ‘small’. Write a program to compute the Newton quotient for the function

f (x) = x²

at the point x = 2 (the exact answer is 4) for values of h starting at 1, and decreasing by a factor of 10 each time (use a for loop). The effect of rounding error becomes apparent when h gets ‘too small’, i.e. less than about 10⁻¹².