If f '(x) = 2x and f(3) = 5, give the tangent line estimate of f(2.8)

Answer 1

since ∆y/∆x ≈ dy/dx we have
∆y ≈ dy/dx * ∆x = 2x * ∆x = 6(-0.2) = -1.2
so f(2.8) ≈ 5 - 1.2 = 3.8

check:
f(x) = x^2-4
f(2.8) = 3.84