Question

Calculating derivative for f(x)² basepoint ______ₐnd moving point ________.

a) At the minimum, at the maximum
b) At the maximum, at the minimum
c) At the critical point, at the endpoint
d) At the endpoint, at the critical point

Answer 1

In physics, the first and second derivatives of potential energy help determine equilibrium stability, and the derivative of velocity defines instantaneous acceleration, indicating maximum or minimum velocity at points where this derivative is zero. Option b.

Step-by-step explanation:

In physics, particularly in the study of mechanics and dynamics, the calculation of derivatives is used to find changes in the system such as velocity, acceleration, and forces.

When discussing equilibrium and stability, the first and second derivatives of potential energy with respect to position can help determine the nature of equilibrium points. For example, if the first derivative of potential energy is negative at x = 0, this position is a relative maximum indicating an unstable equilibrium.

Conversely, if the second derivative of potential energy is positive at x = +xQ, it suggests that these positions are relative minima associated with stable equilibria.

Instantaneous acceleration can be understood as the derivative of the velocity function. The point where the acceleration function has a zero value corresponds to either the maximum or minimum velocity, signifying that at this point, the object is not accelerating or decelerating.

This is closely linked to the concept of critical points which can be related to either the maximum or minimum values of a function, again indicating the stationary points in the motion of an object. Option b.