What is the tangent of 9x-6sqrt(x),\at x=1 ?

The tangent of 9x-6sqrt(x),\at x=1 is y=6x-3

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tangent of 9x-6sqrt(x),\at x=1

tangent of

9 x - 6 x, at x = 1

y = 6 x - 3

Solution steps

Find the tangent point:

(1, 3)

Find the slope of

y = 9 x - 6 x : \frac{d y}{d x} = 9 - \frac{3}{x}

Compute the slope of

y = 9 x - 6 x

x = 1 : m = 6

Find the line with slope m=

6

and passing through

(1, 3) : y = 6 x - 3

y = 6 x - 3

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What is the tangent of 9x-6sqrt(x),\at x=1 ?
The tangent of 9x-6sqrt(x),\at x=1 is y=6x-3