What is the tangent of 5-4x^3 ?

The tangent of 5-4x^3 is y=-12a_{0}^2x+5+8a_{0}^3

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tangent of 5-4x^3

tangent of

5 - 4 x^{3}

y = - 12 a_{0}^{2} x + 5 + 8 a_{0}^{3}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 5 - 4 a_{0}^{3})

Find the slope of

y = 5 - 4 x^{3} : \frac{d y}{d x} = - 12 x^{2}

Compute the slope of

y = 5 - 4 x^{3}

x = a_{0} : m = - 12 a_{0}^{2}

Find the line with slope m=

- 12 a_{0}^{2}

and passing through

(a_{0}, 5 - 4 a_{0}^{3}) : y = - 12 a_{0}^{2} x + 5 + 8 a_{0}^{3}

y = - 12 a_{0}^{2} x + 5 + 8 a_{0}^{3}

{y}

\int \frac{3 x ^{2} 16 + y ^{2}}{y}

x \to 1 lim (3 ln (x))

\frac{2}{2 s ^{2}}

3 x^{2} + 6 x y - 2 y^{2}

What is the tangent of 5-4x^3 ?
The tangent of 5-4x^3 is y=-12a_{0}^2x+5+8a_{0}^3