What is the tangent of y=7+5x^2-2x^3,(2,11) ?

The tangent of y=7+5x^2-2x^3,(2,11) is y=-4x+19

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tangent of y=7+5x^2-2x^3,(2,11)

tangent of

y = 7 + 5 x^{2} - 2 x^{3}, (2, 11)

y = - 4 x + 19

Solution steps

Find the slope of

y = 7 + 5 x^{2} - 2 x^{3} : \frac{d y}{d x} = - 6 x^{2} + 10 x

Compute the slope of

y = 7 + 5 x^{2} - 2 x^{3}

(2, 11) : m = - 4

Find the line with slope m=

- 4

and passing through

(2, 11) : y = - 4 x + 19

y = - 4 x + 19

x \to 2 lim (\frac{x + 4}{x - 2})

\frac{d}{d x} (ln (cos (\frac{1}{x})))

\frac{d y}{d x} = e^{5 x} + 8 y

y^{3} - (2 x + 4) + 3 x y^{2} y^{^{'}} = 0

7 cos (2 x), 7 sin (4 x), x = 0, x = \frac{π}{4}

What is the tangent of y=7+5x^2-2x^3,(2,11) ?
The tangent of y=7+5x^2-2x^3,(2,11) is y=-4x+19