What is the tangent of f(x)=(sqrt(x))/(4x-7),\at x=1 ?

The tangent of f(x)=(sqrt(x))/(4x-7),\at x=1 is y=-11/18 x+5/18

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tangent of f(x)=(sqrt(x))/(4x-7),\at x=1

tangent of

f (x) = \frac{x}{4 x - 7}, at x = 1

y = - \frac{11}{18} x + \frac{5}{18}

Solution steps

Find the tangent point:

(1, - \frac{1}{3})

Find the slope of

f (x) = \frac{x}{4 x - 7} : \frac{df ( x )}{d x} = \frac{- 4 x - 7}{2 x ( 4 x - 7 ) ^{2}}

Compute the slope of

f (x) = \frac{x}{4 x - 7}

x = 1 : m = - \frac{11}{18}

Find the line with slope m=

- \frac{11}{18}

and passing through

(1, - \frac{1}{3}) : y = - \frac{11}{18} x + \frac{5}{18}

y = - \frac{11}{18} x + \frac{5}{18}

- 5 x^{2} + x - 2

\int_{0}^{9} \frac{1}{81 + x ^{2}} d x

y^{^{''}} + 4 y^{^{'}} + 5 y = - 20 e^{t}, y (0) = - 4, y^{^{'}} (0) = 1

\int_{1}^{4} 6 e^{x} d x

f (x, y) = (x)^{2} + (y)^{4}

What is the tangent of f(x)=(sqrt(x))/(4x-7),\at x=1 ?
The tangent of f(x)=(sqrt(x))/(4x-7),\at x=1 is y=-11/18 x+5/18