What is the tangent of f(x)=(x-1)/(2-x),\at x=4 ?

The tangent of f(x)=(x-1)/(2-x),\at x=4 is y= 1/4 x-5/2

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tangent of f(x)=(x-1)/(2-x),\at x=4

tangent of

f (x) = \frac{x - 1}{2 - x}, at x = 4

y = \frac{1}{4} x - \frac{5}{2}

Solution steps

Find the tangent point:

(4, - \frac{3}{2})

Find the slope of

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

Compute the slope of

f (x) = \frac{x - 1}{2 - x}

x = 4 : m = \frac{1}{4}

Find the line with slope m=

\frac{1}{4}

and passing through

(4, - \frac{3}{2}) : y = \frac{1}{4} x - \frac{5}{2}

y = \frac{1}{4} x - \frac{5}{2}

\int (x^{3} - 3 x + x^{- \frac{5}{4}}) d x

x^{^{''}} + 2.25 x^{^{'}} + 0.14 x = 0, x^{^{'}} (0) = 1, x (0) = 2

f (x) = x^{3} - 2 x^{2} - 3 x, (1, - 4)

\frac{\partial}{\partial x} (x y - z)

f (x) = 7 x^{2}

What is the tangent of f(x)=(x-1)/(2-x),\at x=4 ?
The tangent of f(x)=(x-1)/(2-x),\at x=4 is y= 1/4 x-5/2