Given that h(1)=16, and h'(1)=10. Use the linearization of h(x) at x=1 to estimate h(1.1)

Answer 1

Think of this as an algebra 1 problem where you are given a point (1, 16) and a slope (m = 10). Using the point-slope form of a line, we can write: y - y₁ = m(x - x₁) then plugging in (1, 16) as the point (x₁, y₁), we get:

y - 16 = 10(x - 1) or y = 10x + 6. Now, plug in the x-value x = 1.1 to find what y is:

y = 10(1.1) + 6

y = 11 + 6

y = 17