What is the tangent of f(x)=(3x+1)/(x^2+1),(1,2) ?

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

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tangent of f(x)=(3x+1)/(x^2+1),(1,2)

tangent of

f (x) = \frac{3 x + 1}{x ^{2} + 1}, (1, 2)

y = - \frac{1}{2} x + \frac{5}{2}

Solution steps

Find the slope of

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

Compute the slope of

f (x) = \frac{3 x + 1}{x ^{2} + 1}

(1, 2) : m = - \frac{1}{2}

Find the line with slope m=

- \frac{1}{2}

and passing through

(1, 2) : y = - \frac{1}{2} x + \frac{5}{2}

y = - \frac{1}{2} x + \frac{5}{2}

t \to 3 lim (\frac{2 t - 3}{t - 3})

y = 5 sec (x) - 10 cos (x), (\frac{π}{3}, 5)

\int (x - 3) x + 3 d x

f (x) = 4 - x

n = 0 \sum \infty 2^{n + 1} - 2^{n}

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