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}

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{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}

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