What is the tangent of (x-2)^6 ?

The tangent of (x-2)^6 is y=6(a_{0}-2)^5x-5a_{0}^6+48a_{0}^5-180a_{0}^4+320a_{0}^3-240a_{0}^2+64

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tangent of (x-2)^6

tangent of

(x - 2)^{6}

y = 6 (a_{0} - 2)^{5} x - 5 a_{0}^{6} + 48 a_{0}^{5} - 180 a_{0}^{4} + 320 a_{0}^{3} - 240 a_{0}^{2} + 64

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, (a_{0} - 2)^{6})

Find the slope of

y = (x - 2)^{6} : \frac{d y}{d x} = 6 (x - 2)^{5}

Compute the slope of

y = (x - 2)^{6}

x = a_{0} : m = 6 (a_{0} - 2)^{5}

Find the line with slope m=

6 (a_{0} - 2)^{5}

and passing through

(a_{0}, (a_{0} - 2)^{6}) : y = 6 (a_{0} - 2)^{5} x - 5 a_{0}^{6} + 48 a_{0}^{5} - 180 a_{0}^{4} + 320 a_{0}^{3} - 240 a_{0}^{2} + 64

y = 6 (a_{0} - 2)^{5} x - 5 a_{0}^{6} + 48 a_{0}^{5} - 180 a_{0}^{4} + 320 a_{0}^{3} - 240 a_{0}^{2} + 64

x \to 1 lim (3 x - 2)

\int \frac{( sin ( x ) ) ^{3}}{1 + ( cos ( x ) ) ^{3}} d x

\frac{d}{d x} (\frac{5}{5 - x})

\int e^{y} sin (x) d x

(3, 1), (1, - 8)

What is the tangent of (x-2)^6 ?
The tangent of (x-2)^6 is y=6(a_{0}-2)^5x-5a_{0}^6+48a_{0}^5-180a_{0}^4+320a_{0}^3-240a_{0}^2+64