What is the tangent of 5x^2-x^3 ?

The tangent of 5x^2-x^3 is y=(10a_{0}-3a_{0}^2)x+2a_{0}^3-5a_{0}^2

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tangent of 5x^2-x^3

tangent of

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

y = (10 a_{0} - 3 a_{0}^{2}) x + 2 a_{0}^{3} - 5 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 5 a_{0}^{2} - a_{0}^{3})

Find the slope of

y = 5 x^{2} - x^{3} : \frac{d y}{d x} = 10 x - 3 x^{2}

Compute the slope of

y = 5 x^{2} - x^{3}

x = a_{0} : m = 10 a_{0} - 3 a_{0}^{2}

Find the line with slope m=

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

and passing through

(a_{0}, 5 a_{0}^{2} - a_{0}^{3}) : y = (10 a_{0} - 3 a_{0}^{2}) x + 2 a_{0}^{3} - 5 a_{0}^{2}

y = (10 a_{0} - 3 a_{0}^{2}) x + 2 a_{0}^{3} - 5 a_{0}^{2}

f (x) = \frac{1}{x ^{2} + 4}

f (x) = \frac{5 x}{x ^{2} - 4}, at x = 3

x \to 6 lim (x - 6)

\int - 2 tan (x) d x

x \to + 0 lim (\frac{x ^{4}}{x ^{4}})

What is the tangent of 5x^2-x^3 ?
The tangent of 5x^2-x^3 is y=(10a_{0}-3a_{0}^2)x+2a_{0}^3-5a_{0}^2