What is the tangent of f(x)=(3x-5)^{1/2},\at x=2 ?

The tangent of f(x)=(3x-5)^{1/2},\at x=2 is y= 3/2 x-2

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tangent of f(x)=(3x-5)^{1/2},\at x=2

tangent of

f (x) = (3 x - 5)^{\frac{1}{2}}, at x = 2

y = \frac{3}{2} x - 2

Solution steps

Find the tangent point:

(2, 1)

Find the slope of

f (x) = (3 x - 5)^{\frac{1}{2}} : \frac{df ( x )}{d x} = \frac{3}{2 ( 3 x - 5 ) ^{\frac{1}{2}}}

Compute the slope of

f (x) = (3 x - 5)^{\frac{1}{2}}

x = 2 : m = \frac{3}{2}

Find the line with slope m=

\frac{3}{2}

and passing through

(2, 1) : y = \frac{3}{2} x - 2

y = \frac{3}{2} x - 2

\int \frac{1}{( 25 x ^{2} + 16 ) ^{2}} d x

\frac{d}{d x} (- x^{- 2} - 1)

(x^{2} + 4 \cdot x + 2)^{9}

f (x) = \frac{x}{x ^{2} + 196}

f (x) = x^{2} + x + 1

What is the tangent of f(x)=(3x-5)^{1/2},\at x=2 ?
The tangent of f(x)=(3x-5)^{1/2},\at x=2 is y= 3/2 x-2