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

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

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tangent of y=5x-2x^2-x

tangent of

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

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, - 2 a_{0}^{2} + 4 a_{0})

Find the slope of

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

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 = - 4 a_{0} + 4

Find the line with slope m=

- 4 a_{0} + 4

and passing through

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

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

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