What is the tangent of f(x)=3sqrt(x-1),\at x=5 ?

The tangent of f(x)=3sqrt(x-1),\at x=5 is y= 3/4 x+9/4

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tangent of f(x)=3sqrt(x-1),\at x=5

tangent of

f (x) = 3 x - 1, at x = 5

y = \frac{3}{4} x + \frac{9}{4}

Solution steps

Find the tangent point:

(5, 6)

Find the slope of

f (x) = 3 x - 1 : \frac{df ( x )}{d x} = \frac{3}{2 x - 1}

Compute the slope of

f (x) = 3 x - 1

x = 5 : m = \frac{3}{4}

Find the line with slope m=

\frac{3}{4}

and passing through

(5, 6) : y = \frac{3}{4} x + \frac{9}{4}

y = \frac{3}{4} x + \frac{9}{4}

n = 1 \sum \infty \frac{n !}{( 2 n ) !}

x^{4} + \frac{4}{3} x^{3} - 4 x^{2} - \frac{4}{3}

\int \frac{y + 1}{y ^{2} + 1} d y

f (x) = 5 x^{3} - 5 x, (- 1, 0)

g (x) = \frac{1 + 2 x}{3 - 4 x}

What is the tangent of f(x)=3sqrt(x-1),\at x=5 ?
The tangent of f(x)=3sqrt(x-1),\at x=5 is y= 3/4 x+9/4