What is the tangent of f(x)=(x-5)^5,\at x=6 ?

The tangent of f(x)=(x-5)^5,\at x=6 is y=5x-29

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tangent of f(x)=(x-5)^5,\at x=6

tangent of

f (x) = (x - 5)^{5}, at x = 6

y = 5 x - 29

Solution steps

Find the tangent point:

(6, 1)

Find the slope of

f (x) = (x - 5)^{5} : \frac{df ( x )}{d x} = 5 (x - 5)^{4}

Compute the slope of

f (x) = (x - 5)^{5}

x = 6 : m = 5

Find the line with slope m=

5

and passing through

(6, 1) : y = 5 x - 29

y = 5 x - 29

x + \frac{1}{x ^{2}}

\int \frac{x ^{3}}{x ^{2} - 2 x + 1} d x

n = 2 \sum \infty \frac{6}{5 ^{n}}

\int cos^{4} (x s i) n^{3} x d x

\int_{1}^{4} \frac{u - 2}{u} d u

What is the tangent of f(x)=(x-5)^5,\at x=6 ?
The tangent of f(x)=(x-5)^5,\at x=6 is y=5x-29