What is the tangent of y=x^2-6,\at x=a ?

The tangent of y=x^2-6,\at x=a is y=2ax-a^2-6

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tangent of y=x^2-6,\at x=a

tangent of

y = x^{2} - 6, at x = a

y = 2 a x - a^{2} - 6

Solution steps

Find the tangent point:

(a, a^{2} - 6)

Find the slope of

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

Find the line with slope m=

2 a

and passing through

(a, a^{2} - 6) : y = 2 a x - a^{2} - 6

y = 2 a x - a^{2} - 6

What is the tangent of y=x^2-6,\at x=a ?
The tangent of y=x^2-6,\at x=a is y=2ax-a^2-6