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

The tangent of f(x)= 5/(sqrt(x)),\at x=a is y=-5/(2a^{3/2)}x+(15)/(2sqrt(a))

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

tangent of

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

y = - \frac{5}{2 a ^{\frac{3}{2}}} x + \frac{15}{2 a}

Solution steps

Find the tangent point:

(a, \frac{5}{a})

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 = a : m = - \frac{5}{2 a ^{\frac{3}{2}}}

Find the line with slope m=

- \frac{5}{2 a ^{\frac{3}{2}}}

and passing through

(a, \frac{5}{a}) : y = - \frac{5}{2 a ^{\frac{3}{2}}} x + \frac{15}{2 a}

y = - \frac{5}{2 a ^{\frac{3}{2}}} x + \frac{15}{2 a}

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

\int sin^{5} (7 x) cos^{2} (7 x) d x

\int_{- 1}^{1} \frac{5 x}{( 4 + x ^{2} ) ^{2}} d x

\int sinh (4 x + 6) d x

What is the tangent of f(x)= 5/(sqrt(x)),\at x=a ?
The tangent of f(x)= 5/(sqrt(x)),\at x=a is y=-5/(2a^{3/2)}x+(15)/(2sqrt(a))