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Compute Δy and dy for the given values of x and dx = Δx. (Round your answers to three decimal places.). y = 2x − x^2, x = 2, Δx = −0.6. Find: Δy and dy

Respuesta :

y = 2x − x^2 
Differentiating gives: dy/dx =2 -2x 
dy = (2-2x)dx 
If x changes by a small amount (Δx), this will cause y to change by a small amount (Δy). Providing Δx and Δy are small, to a good approximation we can write: 
Δy = (2-2x)Δx 
So if x = 2 and Δx = −0.4: 
Δy = (2-2x2)(-0.4) 
= -2 x (-0.4) 
= 0.8 

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