Explanation:
formally, we see (based on the visible slopes and the y-intercepts) that around x = 2
g(x) = 2x + 1
h(x) = x + 2.5
f(x) = (2x + 1)/(x + 2.5)
f'(x) = (g(x)/h(x))' = (g'(x)×h(x) - g(x)×h'(x)) / h²(x) =
= (2×(x + 2.5) - (2x + 1)×1)/(x + 2.5)² =
= (2x + 5 - 2x - 1)/(x² + 5x + 6.25) =
= 4/(x² + 5x + 6.25)
f'(2) = 4/(2² + 5×2 + 6.25) = 4/20.25 = 0.197530864...