What is the tangent of 4x^2-x^3 ?

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

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tangent of 4x^2-x^3

tangent of

4 x^{2} - x^{3}

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 4 a_{0}^{2} - a_{0}^{3})

Find the slope of

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

Compute the slope of

y = 4 x^{2} - x^{3}

x = a_{0} : m = 8 a_{0} - 3 a_{0}^{2}

Find the line with slope m=

8 a_{0} - 3 a_{0}^{2}

and passing through

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

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

\int_{- \infty}^{0} \frac{1}{5 - 10 x} d x

\int \frac{π}{2}

\frac{d}{d x} ((ln (x))^{4})

f (x) = 3 tan (x)

y = x^{2} - 5 x + 5, (4, 1)

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