   Chapter 13.3, Problem 27E

Chapter
Section
Textbook Problem

# Use Formula 11 to find the curvature.27. y = x428. y = tan x29. y = xex

To determine

To find: The curvature of y=x4 using Formula 11.

Explanation

Given data:

Plane equation is y=x4 .

Formula used:

Consider a plane curve equation in the form of y=f(x) .

Write the expression for curvature according to Formula 11.

k(x)=|f(x)|[1+(f(x))2]32 (1)

Here,

f(x) is function of x,

f(x) is first derivative of function f(x) , and

f(x) is second derivative of function f(x) .

The equation y=x4 indicates y is a function of x. Hence consider y=f(x) .

Write the plane equation.

y=x4

Substitute f(x) for y,

f(x)=x4

Apply differentiation with respect to x on both sides of equation.

f(x)=ddx(x4)=4x41 {ddx(xn)=nxn1}=4x3

Apply differentiation with respect to x on both sides of equation

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