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

The tangent of f(x)= x/(1+5x^2),\at x=3 is y=-11/529 x+135/1058

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tangent of f(x)= x/(1+5x^2),\at x=3

tangent of

f (x) = \frac{x}{1 + 5 x ^{2}}, at x = 3

y = - \frac{11}{529} x + \frac{135}{1058}

Solution steps

Find the tangent point:

(3, \frac{3}{46})

Find the slope of

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

Compute the slope of

f (x) = \frac{x}{1 + 5 x ^{2}}

x = 3 : m = - \frac{11}{529}

Find the line with slope m=

- \frac{11}{529}

and passing through

(3, \frac{3}{46}) : y = - \frac{11}{529} x + \frac{135}{1058}

y = - \frac{11}{529} x + \frac{135}{1058}

y = x + 3

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What is the tangent of f(x)= x/(1+5x^2),\at x=3 ?
The tangent of f(x)= x/(1+5x^2),\at x=3 is y=-11/529 x+135/1058