What is the tangent of f(x)= 9/x ,\at x=2 ?

The tangent of f(x)= 9/x ,\at x=2 is y=-9/4 x+9

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tangent of f(x)= 9/x ,\at x=2

tangent of

f (x) = \frac{9}{x}, at x = 2

y = - \frac{9}{4} x + 9

Solution steps

Find the tangent point:

(2, \frac{9}{2})

Find the slope of

f (x) = \frac{9}{x} : \frac{df ( x )}{d x} = - \frac{9}{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{9}{4}

Find the line with slope m=

- \frac{9}{4}

and passing through

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

y = - \frac{9}{4} x + 9

\int_{1}^{5} x^{2} d x

\frac{d ^{2} y}{d x ^{2}} + y = 1 + x

\int (4 x^{3} - 9 x^{2} + 7 x) e^{- x} d x

\frac{d}{d x} (7 x - 2)

(x + y)^{2} d x + (2 x y + x^{2} - 2) d y = 0, y (1) = 1

What is the tangent of f(x)= 9/x ,\at x=2 ?
The tangent of f(x)= 9/x ,\at x=2 is y=-9/4 x+9