What is the tangent of f(x)=7x-6sqrt(x),\at x=1 ?

The tangent of f(x)=7x-6sqrt(x),\at x=1 is y=4x-3

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tangent of f(x)=7x-6sqrt(x),\at x=1

tangent of

f (x) = 7 x - 6 x, at x = 1

y = 4 x - 3

Solution steps

Find the tangent point:

(1, 1)

Find the slope of

f (x) = 7 x - 6 x : \frac{df ( x )}{d x} = 7 - \frac{3}{x}

Compute the slope of

f (x) = 7 x - 6 x

x = 1 : m = 4

Find the line with slope m=

4

and passing through

(1, 1) : y = 4 x - 3

y = 4 x - 3

x \to 10 lim (12 x)

3 x^{2} y d x + (y + x^{3}) d y = 0

\frac{d}{d x} (ln (\frac{1}{1 + e ^{- x}}))

\frac{d}{d x} (\frac{x}{1 + x ^{\frac{3}{2}}})

\frac{\partial}{\partial x} (\frac{y}{x})

What is the tangent of f(x)=7x-6sqrt(x),\at x=1 ?
The tangent of f(x)=7x-6sqrt(x),\at x=1 is y=4x-3