What is the tangent of y=4x-x^2,\at x=a ?

The tangent of y=4x-x^2,\at x=a is y=(4-2a)x+a^2

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tangent of y=4x-x^2,\at x=a

tangent of

y = 4 x - x^{2}, at x = a

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

Solution steps

Find the tangent point:

(a, 4 a - a^{2})

Find the slope of

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

Find the line with slope m=

4 - 2 a

and passing through

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

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

What is the tangent of y=4x-x^2,\at x=a ?
The tangent of y=4x-x^2,\at x=a is y=(4-2a)x+a^2