What is the tangent of 7x^2-x^3 ?

The tangent of 7x^2-x^3 is y=(14a_{0}-3a_{0}^2)x+2a_{0}^3-7a_{0}^2

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tangent of 7x^2-x^3

tangent of

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

y = (14 a_{0} - 3 a_{0}^{2}) x + 2 a_{0}^{3} - 7 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 7 a_{0}^{2} - a_{0}^{3})

Find the slope of

y = 7 x^{2} - x^{3} : \frac{d y}{d x} = 14 x - 3 x^{2}

Compute the slope of

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

x = a_{0} : m = 14 a_{0} - 3 a_{0}^{2}

Find the line with slope m=

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

and passing through

(a_{0}, 7 a_{0}^{2} - a_{0}^{3}) : y = (14 a_{0} - 3 a_{0}^{2}) x + 2 a_{0}^{3} - 7 a_{0}^{2}

y = (14 a_{0} - 3 a_{0}^{2}) x + 2 a_{0}^{3} - 7 a_{0}^{2}

(x - 2) (4 x + 2)

4^{s i n^{2} (x) + c o s (3 x)}

(\frac{1}{t})^{^{'}}

(e^{\frac{x}{2}})^{^{'}}

x \to 2 + lim (\frac{6}{x - 2})

What is the tangent of 7x^2-x^3 ?
The tangent of 7x^2-x^3 is y=(14a_{0}-3a_{0}^2)x+2a_{0}^3-7a_{0}^2