INSTRUCTOR: Find the curvature of the circle defined by the function y equals 3x squared minus 2x plus 4 at the point x equals 2. Now, there are several formulas we could use for the curvature of a function. The particular formula that I'm going to use is kappa, k, equals the absolute value of y prime, as a numerator, over bracket 1 plus y prime squared close bracket to the 3/2, 3 over 2 exponent.

Because we have our function in terms of x, we can find the derivative of that. So y prime is equal to 6x minus 2, which means the second derivative is equal to 6. And using that formula, k equals absolute value of the second derivative. That'd be 6 divided by a denominator of 1 plus 6x minus 2 squared.

Let me say that again. The denominator is bracket 1 plus open parentheses 6x minus 2 close parentheses squared-- quantity there-- and then all raised to the 3 over 2 power. Let me say that kappa equals as a numerator over the quantity 1 plus parentheses 6x minus 2, close parentheses squared all to the 3 over 2.

If we evaluate this at x equals 2, that tells us that our curvature at that point is equal to 6 over 1 plus 6 times 2 minus 2 quantity squared to the 3 over 2. The curvature at x equals 2 is equal to 6 over 101 to the 2/3, which is approximately 0.0059.