What is the tangent of f(x)=sqrt(3x^3),\at x=3 ?

The tangent of f(x)=sqrt(3x^3),\at x=3 is y= 9/2 x-9/2

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tangent of f(x)=sqrt(3x^3),\at x=3

tangent of

f (x) = 3 x^{3}, at x = 3

y = \frac{9}{2} x - \frac{9}{2}

Solution steps

Find the tangent point:

(3, 9)

Find the slope of

f (x) = 3 x^{3} : \frac{df ( x )}{d x} = \frac{3 3 x ^{\frac{3}{2}}}{2 x ^{2}}

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{9}{2}

Find the line with slope m=

\frac{9}{2}

and passing through

(3, 9) : y = \frac{9}{2} x - \frac{9}{2}

y = \frac{9}{2} x - \frac{9}{2}

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