If \(y = 8x^3 - 3x^2 + 7x - 1\), find \(\frac{d^2y}{dx^2}\).
Question 1 Report
If \(y = 8x^3 - 3x^2 + 7x - 1\), find \(\frac{d^2y}{dx^2}\).
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.
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