What is the tangent of f(x)=sqrt(5x+75),\at x=5 ?

The tangent of f(x)=sqrt(5x+75),\at x=5 is y= 1/4 x+35/4

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tangent of f(x)=sqrt(5x+75),\at x=5

tangent of

f (x) = 5 x + 75, at x = 5

y = \frac{1}{4} x + \frac{35}{4}

Solution steps

Find the tangent point:

(5, 10)

Find the slope of

f (x) = 5 x + 75 : \frac{df ( x )}{d x} = \frac{5}{2 5 x + 75}

Compute the slope of

f (x) = 5 x + 75

x = 5 : m = \frac{1}{4}

Find the line with slope m=

\frac{1}{4}

and passing through

(5, 10) : y = \frac{1}{4} x + \frac{35}{4}

y = \frac{1}{4} x + \frac{35}{4}

\int \frac{1 + 2 x}{1 + x ^{2}} d x

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

\frac{d}{d x} (3 x^{4} - 3 x^{3} - 2)

x \to 1 - lim (3 x)

\frac{d}{d x} (\frac{π}{2 x})

What is the tangent of f(x)=sqrt(5x+75),\at x=5 ?
The tangent of f(x)=sqrt(5x+75),\at x=5 is y= 1/4 x+35/4