Find the value of dy

Question

Find the value of dy and triangleY for y=square root x when x=12 and triangleX=-0.05

triangleY= f(x+ triangleX) - f(x) and dy= f’(x) dx

Answer 1

Given: x = 12, Δx = -0.05

y = f(x) = √x

y' = f'(x) = (1/2)x^-1/2

Δy = f(x + Δx) - f(x) = f(12 - 0.05) - f(12) = f(11.95) - f(12) = √11.95 - √12 = -0.007224412

dy = f'(x) dx = (1/2)x^-1/2 dx = (1/2) (12)^-1/2 (-0.05) = -0.007216878