What is the tangent of f(x)=((3x+5))/(1+x),\at x=1 ?

The tangent of f(x)=((3x+5))/(1+x),\at x=1 is y=-1/2 x+9/2

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tangent of f(x)=((3x+5))/(1+x),\at x=1

tangent of

f (x) = \frac{( 3 x + 5 )}{1 + x}, at x = 1

y = - \frac{1}{2} x + \frac{9}{2}

Solution steps

Find the tangent point:

(1, 4)

Find the slope of

f (x) = \frac{3 x + 5}{1 + x} : \frac{df ( x )}{d x} = - \frac{2}{( 1 + 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{1}{2}

Find the line with slope m=

- \frac{1}{2}

and passing through

(1, 4) : y = - \frac{1}{2} x + \frac{9}{2}

y = - \frac{1}{2} x + \frac{9}{2}

What is the tangent of f(x)=((3x+5))/(1+x),\at x=1 ?
The tangent of f(x)=((3x+5))/(1+x),\at x=1 is y=-1/2 x+9/2