What is the tangent of f(x)=-3x^{3/2},\at x=4 ?

The tangent of f(x)=-3x^{3/2},\at x=4 is y=-9x+12

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tangent of f(x)=-3x^{3/2},\at x=4

tangent of

f (x) = - 3 x^{\frac{3}{2}}, at x = 4

y = - 9 x + 12

Solution steps

Find the tangent point:

(4, - 24)

Find the slope of

f (x) = - 3 x^{\frac{3}{2}} : \frac{df ( x )}{d x} = - \frac{9 x ^{\frac{1}{2}}}{2}

Compute the slope of

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

x = 4 : m = - 9

Find the line with slope m=

- 9

and passing through

(4, - 24) : y = - 9 x + 12

y = - 9 x + 12

\frac{\partial}{\partial x} (x y e^{x})

y^{^{''}} + 8 y^{^{'}} + 20 y = 0, y (0) = 3, y^{^{'}} (0) = - 11

\frac{d}{d x} (- 2 x^{3} + 12 x^{2} - 18 x)

\frac{\partial}{\partial x} (\frac{( 4 x + y )}{x - 3 y})

\frac{d}{d x} (arctan (\frac{x}{2}))

What is the tangent of f(x)=-3x^{3/2},\at x=4 ?
The tangent of f(x)=-3x^{3/2},\at x=4 is y=-9x+12