What is the tangent of f(x)=4sqrt(x),\at x=9 ?

The tangent of f(x)=4sqrt(x),\at x=9 is y= 2/3 x+6

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tangent of f(x)=4sqrt(x),\at x=9

tangent of

f (x) = 4 x, at x = 9

y = \frac{2}{3} x + 6

Solution steps

Find the tangent point:

(9, 12)

Find the slope of

f (x) = 4 x : \frac{df ( x )}{d x} = \frac{2}{x}

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{2}{3}

Find the line with slope m=

\frac{2}{3}

and passing through

(9, 12) : y = \frac{2}{3} x + 6

y = \frac{2}{3} x + 6

5 \frac{d y}{d x} + 2 x = 3

\int \frac{3 x ^{2} + 1}{x ^{3} + x} d x

\frac{d}{d x} f (x) = \frac{2}{5} x^{5} - 4 x^{3} + 9 x^{2} - 6 x - 2

y = 2 x^{- \frac{3}{4}}

t \to 0 lim (\frac{t ^{2} + 9 - 3}{t ^{2}})

What is the tangent of f(x)=4sqrt(x),\at x=9 ?
The tangent of f(x)=4sqrt(x),\at x=9 is y= 2/3 x+6