To find the second derivative of an equation, you use the power rule, which states that for a function f(x) = x^n, the derivative is f'(x) = nx^(n-1). In this case, we have y=3t^3+4t, so the first derivative is y'= 9t^2 + 4. To find the second derivative, we use the power rule again, giving us y''= 18t.
The second derivative is used to find the rate of change of the rate of change of a function. This can give us information about the concavity or curvature of the graph, as well as the points where the function has a maximum or minimum value.
To evaluate the second derivative at a specific point, simply plug in the desired value for t into the equation for the second derivative, y''= 18t. For example, if we wanted to find the second derivative at t=2, we would have y''=18(2)=36.
Yes, the second derivative can be negative. This means that the graph of the function is concave down at that point. A negative second derivative can also indicate that the function has a relative maximum at that point.
The second derivative is the derivative of the first derivative, which is the derivative of the original function. This means that the second derivative is a measure of the curvature of the graph of the original function. A positive second derivative indicates a concave up graph, while a negative second derivative indicates a concave down graph.