If y = 8x3 3 - 3x2 2 + 7x - 1, find d2ydx2 d 2 y d x 2 .

If y = 8x${}^3$ - 3x${}^2$ + 7x - 1, find $\frac{d^{2}y}{d{x}^2}$.

Answer Details

To find d2y/dx2, we need to take the second derivative of y with respect to x. dy/dx = 24x^2 - 6x + 7 Taking the derivative of dy/dx, we get: d2y/dx2 = 48x - 6 Therefore, the answer is 48x - 6. To understand this, we need to remember that the second derivative of a function gives us the rate of change of the slope of the function. In this case, the first derivative of y gives us the slope of the function, and the second derivative gives us the rate of change of that slope.