Question

Consider the equation 0.79 y²=x³-2.24 x²+x. In this question you will calculate the second derivative, d² y/d x² for the following point

x=0.06, y=0.26

Answer 1

To find the second derivative, take the derivative of the first derivative. Substitute the given values to calculate the second derivative.

Step-by-step explanation:

To find the second derivative, d²y/dx², we need to take the derivative of the first derivative. The first derivative, dy/dx, can be found by implicitly differentiating the equation 0.79y² = x³ - 2.24x² + x. Differentiating both sides with respect to x, we get 1.58y(dy/dx) = 3x² - 4.48x + 1. Now, let's find the second derivative by differentiating dy/dx again with respect to x. Differentiating the equation 1.58y(dy/dx) = 3x² - 4.48x + 1, we get 1.58(dy/dx)² + 1.58y(d²y/dx²) = 6x - 4.48. Since we need to find d²y/dx² at the point (x = 0.06, y = 0.26), substitute these values into the equation to calculate the second derivative.