Final answer:
To estimate the value of g(1.2), use the linear approximation formula with g(1) and g'(1).
Step-by-step explanation:
To estimate the value of g(1.2), we can use the derivative g'(1) to find the slope of the tangent line at x = 1. Then, we can use this slope to find the approximate value of g(1.2) by using the formula for a linear approximation:
g(x) ≈ g(1) + g'(1)(x - 1)
Plugging in the given values of g(1) = -17 and g'(1) = 5, we have:
g(1.2) ≈ -17 + 5(1.2 - 1) = -17 + 5(0.2) = -17 + 1 = -16