Michael K. answered • 06/12/19

PhD professional for Math, Physics, and Computer Tutoring

Given that y'(8) = 1/12, we will use this value as the slope (since a derivative is a tangent which is the generalization of a slope -- linear approximation -- at a point).

So m = 1/12

Our line equation then becomes...

y = mx + b

Since we want to know how much y changes between x = 8 and x = 8.12, we have Δx = 0.12

y_{1} = mx_{1} + b

y_{2} = mx_{2} + b

y_{2} - y_{1} = m * (x_{2} - x_{1})

But this is nothing more than the "change in y" related to the "change in x"

Δy = m Δx

Δy = 1/12 * 0.12 = 1/12 * 12/100 = 1/100 = 0.01