What is the tangent of f(x)= 7/(sqrt(x)),(4, 7/2) ?

The tangent of f(x)= 7/(sqrt(x)),(4, 7/2) is y=-7/16 x+21/4

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tangent of f(x)= 7/(sqrt(x)),(4, 7/2)

tangent of

f (x) = \frac{7}{x}, (4, \frac{7}{2})

y = - \frac{7}{16} x + \frac{21}{4}

Solution steps

Find the slope of

f (x) = \frac{7}{x} : \frac{df ( x )}{d x} = - \frac{7}{2 x ^{\frac{3}{2}}}

Compute the slope of

f (x) = \frac{7}{x}

(4, \frac{7}{2}) : m = - \frac{7}{16}

Find the line with slope m=

- \frac{7}{16}

and passing through

(4, \frac{7}{2}) : y = - \frac{7}{16} x + \frac{21}{4}

y = - \frac{7}{16} x + \frac{21}{4}

\frac{d y}{d x} - 2 y = e^{5 x}

\frac{d}{d x} (- 5 sin (2 x))

\frac{d}{d x} (cos (x + 1))

x^{2} y^{^{''}} - 4 x y^{^{'}} - 36 y = 0

\frac{\partial}{\partial x} (x y cos (3 x) + e^{x y})

What is the tangent of f(x)= 7/(sqrt(x)),(4, 7/2) ?
The tangent of f(x)= 7/(sqrt(x)),(4, 7/2) is y=-7/16 x+21/4