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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

(a) Use the formula in Exercise 69(b) to find the curvature of the parabola y = x2 at the point (1,1).

(b) At what point does this parabola have maximum curvature?

(a)

To determine

The curvature of the parabola y=x2 at the point (1,1).

Explanation

Formula used:

The curvature formula is κ=|d2ydx2|[1+(dydx)2]32 for the parametric curve x=x and y=f(x).

Calculation:

Differentiate y=x2 with respect to x,

dydx=2x

Differentiate dydx=2x with respect to x,

d2ydx2=2

Substitute dydx=2x and d2ydx2=2 in above mentioned curvature formula

(b)

To determine

The point at which the parabola y=x2 has maximum curvature.

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