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Chapter 11: Q. 15 (page 889)

Show that the second derivative of the function of y = x2is constant, but its curvature varies with x

Short Answer

Expert verified

The second derivative of the function is 2 which is constant.

k depends on x thus the curvature varies with x.

Step by step solution

01

Step 1. Given information.

We have to show that the second derivative of the function of y = x2is constant, but its curvature varies with x

02

Step 2. Explanation.

Let y=x2

then,

y鈥�=2xandy鈥测赌�=2

Thus the second derivative of the function is 2 which is constant.

Curvature :

If y=f(x) is a twice-differentiable function then the curvature of f is given by

k=f鈥测赌�(x)1+f鈥�(x)232

Substituting f鈥�&f鈥测赌�values in the above formula, we get :

k=|2|1+(2x)232k=21+4x232

k depends on x thus the curvature varies with x.

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