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

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

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

tangent of

f (x) = \frac{1}{x}, at x = \frac{1}{4}

y = - 4 x + 3

Solution steps

Find the tangent point:

(\frac{1}{4}, 2)

Find the slope of

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

Compute the slope of

f (x) = \frac{1}{x}

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

Find the line with slope m=

- 4

and passing through

(\frac{1}{4}, 2) : y = - 4 x + 3

y = - 4 x + 3

\int (ln (t)) d t

\frac{8}{( x ^{2} + 4 )}

\frac{d}{d x} (lo g_{2} ((x - 1)^{3}))

f (x) = x \cdot e^{- x + 1}

4 + 5 x^{2} - 2 x^{3}

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