What is the tangent of y=x^3+2,(2,2) ?

The tangent of y=x^3+2,(2,2) is y=2 \lor y=27x-52

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tangent of y=x^3+2,(2,2)

tangent of

y = x^{3} + 2, (2, 2)

y = 2 or y = 27 x - 52

Solution steps

Slope of the tangent line at

(2, 2) : m = \frac{x ^{3}}{x - 2}

Find the slope of

y = x^{3} + 2 : m = 3 x^{2}

Solve

3 x^{2} = \frac{x ^{3}}{x - 2} : x = 0, x = 3

Find the tangent line at

x = 0 : y = 2

Find the tangent line at

x = 3 : y = 27 x - 52

y = 2 or y = 27 x - 52

What is the tangent of y=x^3+2,(2,2) ?
The tangent of y=x^3+2,(2,2) is y=2 \lor y=27x-52