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

The tangent of f(x)= 4/(5x+1),\at x=-1 is y=-5/4 x-9/4

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

tangent of

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

y = - \frac{5}{4} x - \frac{9}{4}

Solution steps

Find the tangent point:

(- 1, - 1)

Find the slope of

f (x) = \frac{4}{5 x + 1} : \frac{df ( x )}{d x} = - \frac{20}{( 5 x + 1 ) ^{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}{4}

Find the line with slope m=

- \frac{5}{4}

and passing through

(- 1, - 1) : y = - \frac{5}{4} x - \frac{9}{4}

y = - \frac{5}{4} x - \frac{9}{4}

What is the tangent of f(x)= 4/(5x+1),\at x=-1 ?
The tangent of f(x)= 4/(5x+1),\at x=-1 is y=-5/4 x-9/4