What is the tangent of f(x)=3x^{-2},\at x=4 ?

The tangent of f(x)=3x^{-2},\at x=4 is y=-3/32 x+9/16

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tangent of f(x)=3x^{-2},\at x=4

tangent of

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

y = - \frac{3}{32} x + \frac{9}{16}

Solution steps

Find the tangent point:

(4, \frac{3}{16})

Find the slope of

f (x) = 3 x^{- 2} : \frac{df ( x )}{d x} = - \frac{6}{x ^{3}}

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{3}{32}

Find the line with slope m=

- \frac{3}{32}

and passing through

(4, \frac{3}{16}) : y = - \frac{3}{32} x + \frac{9}{16}

y = - \frac{3}{32} x + \frac{9}{16}

What is the tangent of f(x)=3x^{-2},\at x=4 ?
The tangent of f(x)=3x^{-2},\at x=4 is y=-3/32 x+9/16