Question

Compute Δy and dy for the given values of x and dx = Δx.

Compute Δy and dy for the given values of x and dx = Δx.

y = x2 − 6x, x = 5, Δx = 0.5

Answer 1

• ∆y = 2.25
• dy = 2.0

Explanation:

You want values of ∆y and dy for y = x² -6x and x = 5, ∆x = dx = 0.5.

Dy

The value of dy is found by differentiating the function.

y = x² -6x

dy = (2x -6)dx

For x=5, dx=0.5, this is ...

dy = (2·5 -6)(0.5) = (4)(0.5)

dy = 2

∆y

The value of ∆y is the function difference ...

∆y = f(x +∆x) -f(x) . . . . . . . where y = f(x) = x² -6x

∆y = (5.5² -6(5.5)) -(5² -6·5)

∆y = (30.25 -33) -(25 -30) = -2.75 +5

∆y = 2.25

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Additional comment

On the attached graph, ∆y is the difference between function values:

∆y = -2.75 -(-5) = 2.25

and dy is the difference between the linearized function value and the function value:

dy = -3 -(-5) = 2.00

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