What is the tangent of f(x)=sqrt(5-3x),\at x= 1/3 ?

The tangent of f(x)=sqrt(5-3x),\at x= 1/3 is y=-3/4 x+9/4

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tangent of f(x)=sqrt(5-3x),\at x= 1/3

tangent of

f (x) = 5 - 3 x, at x = \frac{1}{3}

y = - \frac{3}{4} x + \frac{9}{4}

Solution steps

Find the tangent point:

(\frac{1}{3}, 2)

Find the slope of

f (x) = 5 - 3 x : \frac{df ( x )}{d x} = - \frac{3}{2 5 - 3 x}

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}{4}

Find the line with slope m=

- \frac{3}{4}

and passing through

(\frac{1}{3}, 2) : y = - \frac{3}{4} x + \frac{9}{4}

y = - \frac{3}{4} x + \frac{9}{4}

What is the tangent of f(x)=sqrt(5-3x),\at x= 1/3 ?
The tangent of f(x)=sqrt(5-3x),\at x= 1/3 is y=-3/4 x+9/4