What is the normal of y=x^3-2x^2+5,(2,5) ?

The normal of y=x^3-2x^2+5,(2,5) is y=-1/4 x+11/2

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normal of y=x^3-2x^2+5,(2,5)

normal of

y = x^{3} - 2 x^{2} + 5, (2, 5)

y = - \frac{1}{4} x + \frac{11}{2}

Solution steps

Find the slope of

y = x^{3} - 2 x^{2} + 5 : \frac{d y}{d x} = 3 x^{2} - 4 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 = 4

Compute the slope of the perpendicular line:

m_{p} = - \frac{1}{4}

Find the line with slope m=

- \frac{1}{4}

and passing through

(2, 5) : y = - \frac{1}{4} x + \frac{11}{2}

y = - \frac{1}{4} x + \frac{11}{2}

\int \frac{1}{3 x ^{4}} d x

\int_{- 1}^{1} \frac{1}{2} (4 - 4 x^{2})^{2} d x

\int_{1}^{100} \frac{29}{x ^{3}} d x

\frac{\partial}{\partial t} (\frac{s - 3 r}{t})

x \to 0 lim (3^{\frac{1}{x}})

What is the normal of y=x^3-2x^2+5,(2,5) ?
The normal of y=x^3-2x^2+5,(2,5) is y=-1/4 x+11/2