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Let ℓ be the tangent line to the curve y = 2x³ at the point (1, 2). The angle of inclination of ℓ is the angle ϕ that ℓ makes with the positive direction of the x-axis.
Calculate ϕ correct to the nearest degree.

Respuesta :

Answer:

Approximately 83 degrees

Step-by-step explanation:

Consider the curve

[tex]y=2x^3\\[/tex]

Let us find equation of tangent or slope of tangent at (1,2)

Differentiate y wrt x

[tex]y' = 8x^2[/tex]

slope of tangent = value of derivative at that point

So slope of tangent at (1,2) = [tex]8(1^2) = 8[/tex]

Slope of a line is nothing but tangent of the angle it makes with positive x axis

So if phi is the angle

we have

[tex]tan \phi =8\\\phi = arctan 8\\= 82.875[/tex]

Approximately 83 degrees

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