AP Calculus BC - Linearization

Question

Find the linearization of the given function centered at x = a, use it to estimate f(b).

f(x) = sqrt(17 sin(x)), a = π/6, b = 0.5

Answer 1

Answer 2

f(x) = √(17sinx); f(π/6) = √8.5; f'(x) = √17cosx/(2√sinx); f'(π/6) = √17·(√3/2)/(√2) = √102/4

L(x) = √8.5 + √102/4(x - π/6)

f(0.5) ≈ L(0.5) = √8.5 + √102/4(0.5 - π/6) = 2.97506