What is the tangent of f(x)=3x^{1/2}+x^{3/2},\at x=9 ?

The tangent of f(x)=3x^{1/2}+x^{3/2},\at x=9 is y=5x-9

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tangent of f(x)=3x^{1/2}+x^{3/2},\at x=9

tangent of

f (x) = 3 x^{\frac{1}{2}} + x^{\frac{3}{2}}, at x = 9

y = 5 x - 9

Solution steps

Find the tangent point:

(9, 36)

Find the slope of

f (x) = 3 x^{\frac{1}{2}} + x^{\frac{3}{2}} : \frac{df ( x )}{d x} = \frac{3}{2 x ^{\frac{1}{2}}} + \frac{3 x ^{\frac{1}{2}}}{2}

Compute the slope of

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

x = 9 : m = 5

Find the line with slope m=

5

and passing through

(9, 36) : y = 5 x - 9

y = 5 x - 9

\int 6 sin (2 t) d t

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

f (x) = (x^{3} + 3 x^{2} + 1)^{- 3}

x \to \infty lim (2 - 1)

\int (x^{2} - 9) d x

What is the tangent of f(x)=3x^{1/2}+x^{3/2},\at x=9 ?
The tangent of f(x)=3x^{1/2}+x^{3/2},\at x=9 is y=5x-9