What is the tangent of f(x)=6x-32sqrt(x),\at x=4 ?

The tangent of f(x)=6x-32sqrt(x),\at x=4 is y=-2x-32

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tangent of f(x)=6x-32sqrt(x),\at x=4

tangent of

f (x) = 6 x - 32 x, at x = 4

y = - 2 x - 32

Solution steps

Find the tangent point:

(4, - 40)

Find the slope of

f (x) = 6 x - 32 x : \frac{df ( x )}{d x} = 6 - \frac{16}{x}

Compute the slope of

f (x) = 6 x - 32 x

x = 4 : m = - 2

Find the line with slope m=

- 2

and passing through

(4, - 40) : y = - 2 x - 32

y = - 2 x - 32

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What is the tangent of f(x)=6x-32sqrt(x),\at x=4 ?
The tangent of f(x)=6x-32sqrt(x),\at x=4 is y=-2x-32