What is the tangent of f(x)=x^2-9x,\at P(x)=3,-15 ?

The tangent of f(x)=x^2-9x,\at P(x)=3,-15 is y=(2a_{0}-9)x-a_{0}^2

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tangent of f(x)=x^2-9x,\at P(x)=3,-15

tangent of

f (x) = x^{2} - 9 x, at P (x) = 3, - 15

y = (2 a_{0} - 9) x - a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{2} - 9 a_{0})

Find the slope of

f (x) = x^{2} - 9 x : \frac{df ( x )}{d x} = 2 x - 9

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_{0} - 9

Find the line with slope m=

2 a_{0} - 9

and passing through

(a_{0}, a_{0}^{2} - 9 a_{0}) : y = (2 a_{0} - 9) x - a_{0}^{2}

y = (2 a_{0} - 9) x - a_{0}^{2}

y = x^{4} + 8 e^{x}, (0, 8)

\frac{d}{d x} (c x e^{2 x})

\int sin (21 x) \cdot sin (2 x) \cdot sin (x) d x

x \to 3 - lim (x^{3} - 3 x - 7)

(x^{2} - 4) y^{^{'}} = - 2 x y^{2}

What is the tangent of f(x)=x^2-9x,\at P(x)=3,-15 ?
The tangent of f(x)=x^2-9x,\at P(x)=3,-15 is y=(2a_{0}-9)x-a_{0}^2