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

The tangent of f(x)= 5/x ,\at x=4,x=5 is y=-5/16 x+5/2

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

tangent of

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

y = - \frac{5}{16} x + \frac{5}{2}

Solution steps

Find the tangent point:

(4, \frac{5}{4})

Find the slope of

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

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = - \frac{5}{16}

Find the line with slope m=

- \frac{5}{16}

and passing through

(4, \frac{5}{4}) : y = - \frac{5}{16} x + \frac{5}{2}

y = - \frac{5}{16} x + \frac{5}{2}

What is the tangent of f(x)= 5/x ,\at x=4,x=5 ?
The tangent of f(x)= 5/x ,\at x=4,x=5 is y=-5/16 x+5/2