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

The tangent of 3x^2-x^3 is y=(6a_{0}-3a_{0}^2)x+2a_{0}^3-3a_{0}^2

Popular >

tangent of 3x^2-x^3

tangent of

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

y = (6 a_{0} - 3 a_{0}^{2}) x + 2 a_{0}^{3} - 3 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

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

x = a_{0} : m = 6 a_{0} - 3 a_{0}^{2}

Find the line with slope m=

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

and passing through

(a_{0}, 3 a_{0}^{2} - a_{0}^{3}) : y = (6 a_{0} - 3 a_{0}^{2}) x + 2 a_{0}^{3} - 3 a_{0}^{2}

y = (6 a_{0} - 3 a_{0}^{2}) x + 2 a_{0}^{3} - 3 a_{0}^{2}

\frac{\partial}{\partial x} (3 x^{2} + y^{2})

\int_{x}^{3} sin (t^{2}) d t

\frac{d}{d x} (\frac{50}{x ^{7}})

\frac{d y}{d x} (x 16 - x) = 0

4 e^{- 7 t} cos (9 t)

What is the tangent of 3x^2-x^3 ?
The tangent of 3x^2-x^3 is y=(6a_{0}-3a_{0}^2)x+2a_{0}^3-3a_{0}^2