What is the tangent of 2/(sqrt(x)),\at x= 1/4 ?

The tangent of 2/(sqrt(x)),\at x= 1/4 is y=-8x+6

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tangent of 2/(sqrt(x)),\at x= 1/4

tangent of

\frac{2}{x}, at x = \frac{1}{4}

y = - 8 x + 6

Solution steps

Find the tangent point:

(\frac{1}{4}, 4)

Find the slope of

y = \frac{2}{x} : \frac{d y}{d x} = - \frac{1}{x ^{\frac{3}{2}}}

Compute the slope of

y = \frac{2}{x}

x = \frac{1}{4} : m = - 8

Find the line with slope m=

- 8

and passing through

(\frac{1}{4}, 4) : y = - 8 x + 6

y = - 8 x + 6

y = \frac{- 2 x}{x ^{2} + 1}, (1, - 1)

x \to 5 lim (3 x^{2} - 2 x - 7)

f (x) = 2 x^{2} + 5 x - 3, (1, 4)

\frac{d}{d x} (A x e^{- x} cos (2 x) + B x e^{- x} sin (2 x))

\int_{- 2}^{3} \frac{4}{x ^{4}} d x

What is the tangent of 2/(sqrt(x)),\at x= 1/4 ?
The tangent of 2/(sqrt(x)),\at x= 1/4 is y=-8x+6