please help. Compute Δy and dy for x = 4 and dx = Δx = -0.2. (Round the answers to three decimal places.)
y = 4x - x2....im lost to were to start solving for delta y
To find Δy, we need to calculate the change in y when x is changed by Δx. In this case, we are given x = 4 and Δx = -0.2.
To begin, let's find the value of y for x = 4 using the given equation y = 4x - x^2.
Substituting x = 4 into the equation:
y = 4(4) - (4)^2
y = 16 - 16
y = 0
So, when x = 4, y = 0.
Now, we can find the value of y for x = 4 + Δx = 4 - 0.2 = 3.8.
Substituting x = 3.8 into the equation:
y = 4(3.8) - (3.8)^2
y = 15.2 - 14.44
y ≈ 0.76
When x is changed by -0.2, y changes by approximately 0.76.
Therefore, Δy ≈ 0.76 and dy ≈ 0.76.
To find Δy and dy for x = 4 and dx = Δx = -0.2 in the equation y = 4x - x^2, you need to follow these steps:
Step 1: Substitute the given values of x and dx into the equation.
y = 4(4) - (4)^2
y = 16 - 16
y = 0
Step 2: Calculate the y-value for x + Δx.
y' = 4(4 - 0.2) - (4 - 0.2)^2
y' = 4(3.8) - (3.8)^2
y' = 15.2 - 14.44
y' = 0.76
Step 3: Compute Δy by subtracting y from y'.
Δy = y' - y
Δy = 0.76 - 0
Δy = 0.76
Step 4: Calculate dy by multiplying Δx by the derivative of y with respect to x.
dy = (dy/dx) * (Δx)
To find dy/dx, differentiate the equation y = 4x - x^2 with respect to x:
dy/dx = 4 - 2x
Now, substitute x = 4 into dy/dx:
dy = (4 - 2(4)) * (-0.2)
dy = (4 - 8) * (-0.2)
dy = (-4) * (-0.2)
dy = 0.8
Therefore, Δy = 0.76 and dy = 0.8 when x = 4 and dx = Δx = -0.2 in the equation y = 4x - x^2.
To compute for dy, you use the equation dy=f'(a)*dx where f'(a) is the derivative of the function given.
So dy=(4-2x)*dx Plug in the values
dy=(4-2(4))*(-.2)=? SOLVE
To find Δ y, you use the equation
Δy=f(x-Δx)-f(x) Plug in the values
Δy=(4(4.2)-(4.2)^2)-(4(4)-4^2)=? SOLVE