What is the tangent of f(x)=(x-2)^{1/2},\at x=6 ?

The tangent of f(x)=(x-2)^{1/2},\at x=6 is y= 1/4 x+1/2

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tangent of f(x)=(x-2)^{1/2},\at x=6

tangent of

f (x) = (x - 2)^{\frac{1}{2}}, at x = 6

y = \frac{1}{4} x + \frac{1}{2}

Solution steps

Find the tangent point:

(6, 2)

Find the slope of

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

Compute the slope of

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

x = 6 : m = \frac{1}{4}

Find the line with slope m=

\frac{1}{4}

and passing through

(6, 2) : y = \frac{1}{4} x + \frac{1}{2}

y = \frac{1}{4} x + \frac{1}{2}

\int 5 sin^{3} (x) d x

t \to 1 lim (sin (- 3 π t))

y = e^{c o s (3) x^{2}}

x^{2} + x y + 2 y^{2} = 4, (1, 1)

f (x) = 2 x^{6} + 3 x

What is the tangent of f(x)=(x-2)^{1/2},\at x=6 ?
The tangent of f(x)=(x-2)^{1/2},\at x=6 is y= 1/4 x+1/2