What is the tangent of f(x)= 5/(sqrt(x)),\at x= 1/4 ?

The tangent of f(x)= 5/(sqrt(x)),\at x= 1/4 is y=-20x+15

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tangent of f(x)= 5/(sqrt(x)),\at x= 1/4

tangent of

f (x) = \frac{5}{x}, at x = \frac{1}{4}

y = - 20 x + 15

Solution steps

Find the tangent point:

(\frac{1}{4}, 10)

Find the slope of

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

Compute the slope of

f (x) = \frac{5}{x}

x = \frac{1}{4} : m = - 20

Find the line with slope m=

- 20

and passing through

(\frac{1}{4}, 10) : y = - 20 x + 15

y = - 20 x + 15

\int (y - x) d x

x \to - 1 lim (\frac{x ^{2} - 1}{x - 1})

\int \frac{2 v ^{3} - v}{v ^{4} - v ^{2}} d v

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

\int \frac{( e ^{2 x} )}{49 + e ^{4 x}} d x

What is the tangent of f(x)= 5/(sqrt(x)),\at x= 1/4 ?
The tangent of f(x)= 5/(sqrt(x)),\at x= 1/4 is y=-20x+15