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

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

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

tangent of

\frac{2 x ^{\frac{3}{2}} - x ^{2} + 4}{x}, at x = 4

y = - \frac{3}{4} x + 4

Solution steps

Find the tangent point:

(4, 1)

Find the slope of

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

Find the line with slope m=

- \frac{3}{4}

and passing through

(4, 1) : y = - \frac{3}{4} x + 4

y = - \frac{3}{4} x + 4

\frac{d}{d x} (\frac{7}{3 x ^{4}})

x \to 8 lim (\frac{x - 8}{x})

x \to \infty lim (\frac{6 x ^{2}}{e ^{5 x}})

\frac{\partial}{\partial x} (ln ∣ x y ∣)

y^{^{'}} sin (3 π x) = π y cos (3 π x)

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