Suppose that f(4)=9 and f′(4)=−0.66. Use this information to estimate f(4.1). f(4.1)≈

Answer 1

f(4) = 9, m = f'(4) = -0.66

y - y₀ = m(x-x₀)

y-9=-0.66(x-4) = -0.66x + 2.64

y(x) = -0.66x+11.64

y(4.1) ≈ -0.66(4.1)+11.64

≈ -2.706+11.64

≈ 8.934