What is the tangent of y=3+4x^2-2x^3,\at x=a ?

The tangent of y=3+4x^2-2x^3,\at x=a is y=(-6a^2+8a)x+4a^3-4a^2+3

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tangent of y=3+4x^2-2x^3,\at x=a

tangent of

y = 3 + 4 x^{2} - 2 x^{3}, at x = a

y = (- 6 a^{2} + 8 a) x + 4 a^{3} - 4 a^{2} + 3

Solution steps

Find the tangent point:

(a, 3 + 4 a^{2} - 2 a^{3})

Find the slope of

y = 3 + 4 x^{2} - 2 x^{3} : \frac{d y}{d x} = - 6 x^{2} + 8 x

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = - 6 a^{2} + 8 a

Find the line with slope m=

- 6 a^{2} + 8 a

and passing through

(a, 3 + 4 a^{2} - 2 a^{3}) : y = (- 6 a^{2} + 8 a) x + 4 a^{3} - 4 a^{2} + 3

y = (- 6 a^{2} + 8 a) x + 4 a^{3} - 4 a^{2} + 3

x \to \infty lim ((\frac{1}{x})^{\frac{2}{x}})

y^{^{''}} + 5 t y^{^{'}} - 5 y = 0

\frac{d}{d x} (ln (cosh (x)))

\frac{\partial}{\partial y} (x cos (y) + y e^{x})

\frac{d}{d x} (\frac{x ^{2} - 1}{2 x})

What is the tangent of y=3+4x^2-2x^3,\at x=a ?
The tangent of y=3+4x^2-2x^3,\at x=a is y=(-6a^2+8a)x+4a^3-4a^2+3