What is the tangent of 14x-3x^2 ?

The tangent of 14x-3x^2 is y=(14-6a_{0})x+3a_{0}^2

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tangent of 14x-3x^2

tangent of

14 x - 3 x^{2}

y = (14 - 6 a_{0}) x + 3 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 14 a_{0} - 3 a_{0}^{2})

Find the slope of

y = 14 x - 3 x^{2} : \frac{d y}{d x} = 14 - 6 x

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = 14 - 6 a_{0}

Find the line with slope m=

14 - 6 a_{0}

and passing through

(a_{0}, 14 a_{0} - 3 a_{0}^{2}) : y = (14 - 6 a_{0}) x + 3 a_{0}^{2}

y = (14 - 6 a_{0}) x + 3 a_{0}^{2}

\int \frac{3 x + 4}{x ^{2} + 3 x + 2} d x

\int (4 x - x^{2}) d x

\frac{\partial}{\partial x} (- 2 sin (2 x))

arcsec (3 x)

y^{^{'}} = x^{2} y

What is the tangent of 14x-3x^2 ?
The tangent of 14x-3x^2 is y=(14-6a_{0})x+3a_{0}^2