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

The tangent of 5x-2x^2 is y=(5-4a_{0})x+2a_{0}^2

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tangent of 5x-2x^2

tangent of

5 x - 2 x^{2}

y = (5 - 4 a_{0}) x + 2 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}^{2})

Find the slope of

y = 5 x - 2 x^{2} : \frac{d y}{d x} = 5 - 4 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 = 5 - 4 a_{0}

Find the line with slope m=

5 - 4 a_{0}

and passing through

(a_{0}, 5 a_{0} - 2 a_{0}^{2}) : y = (5 - 4 a_{0}) x + 2 a_{0}^{2}

y = (5 - 4 a_{0}) x + 2 a_{0}^{2}

\frac{d}{d x} (e^{e x})

\int \frac{4 - x}{16 - x ^{2}} d x

d er i v a t i v e f (x) = 5 (9 x^{7} + 3 x^{4} - 2)^{3}

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

\int \frac{x ^{4} + 5 x - 3}{x ^{2}} d x

What is the tangent of 5x-2x^2 ?
The tangent of 5x-2x^2 is y=(5-4a_{0})x+2a_{0}^2