What is the tangent of y=5+5x^2-2x^3,(2,9) ?

The tangent of y=5+5x^2-2x^3,(2,9) is y=-4x+17

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tangent of y=5+5x^2-2x^3,(2,9)

tangent of

y = 5 + 5 x^{2} - 2 x^{3}, (2, 9)

y = - 4 x + 17

Solution steps

Find the slope of

y = 5 + 5 x^{2} - 2 x^{3} : \frac{d y}{d x} = - 6 x^{2} + 10 x

Compute the slope of

y = 5 + 5 x^{2} - 2 x^{3}

(2, 9) : m = - 4

Find the line with slope m=

- 4

and passing through

(2, 9) : y = - 4 x + 17

y = - 4 x + 17

\frac{d y}{d x} = y - y^{3}

(0, - 2), (- 2, - 2)

x \to 0 lim (2 cos (2 x))

x \to 4 - lim (\frac{6}{x - 4})

x^{2} + 7

What is the tangent of y=5+5x^2-2x^3,(2,9) ?
The tangent of y=5+5x^2-2x^3,(2,9) is y=-4x+17