What is the tangent of f(x)= 3/(sqrt(x)),\at x=4 ?

The tangent of f(x)= 3/(sqrt(x)),\at x=4 is y=-3/16 x+9/4

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tangent of f(x)= 3/(sqrt(x)),\at x=4

tangent of

f (x) = \frac{3}{x}, at x = 4

y = - \frac{3}{16} x + \frac{9}{4}

Solution steps

Find the tangent point:

(4, \frac{3}{2})

Find the slope of

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

Compute the slope of

f (x) = \frac{3}{x}

x = 4 : m = - \frac{3}{16}

Find the line with slope m=

- \frac{3}{16}

and passing through

(4, \frac{3}{2}) : y = - \frac{3}{16} x + \frac{9}{4}

y = - \frac{3}{16} x + \frac{9}{4}

\frac{d x}{d t} = x e^{t} + 3 e^{t} + x - 3

15 cos (x), 15 sin (x), [0, \frac{π}{2}]

\int sin (2 x) cos (5 x) d x

x + 3, \frac{( x + 3 )}{2}, - 3, 1

\frac{d}{d x} (4 x \cdot sin (x))

What is the tangent of f(x)= 3/(sqrt(x)),\at x=4 ?
The tangent of f(x)= 3/(sqrt(x)),\at x=4 is y=-3/16 x+9/4