Limits and Continuity

Given a function $g(t)$ with two local maxima at $t=2$ and $t=5$, which method would be most appropriate to determine the absolute maximum value of $g(t)$ over the closed interval [1,6]?

m(x) represents the total amount of interest gained by a bank account, where x is the number of years. What does m(20) represent?

If the velocity of an object moving along a straight path is given by $v(t) = 3t^2 - 6t + 4$, what is the total displacement of the object from time $t = 0$ to $t = 3$?

Which of the following is the same as the slope of the tangent line to a curve at a specific point?

Which rates of change depend on the concept of limits?

Which describes why a continuous function does not guarantee differentiability at every point on its domain?

The height of a ball thrown in the air is given by the function $h(t) = -16t^2 + 64t$, where $h(t)$ represents the height (in feet) at time $t$ (in seconds). Calculate the average rate of change of the position from $t = 0$ to $t = 3$.

If $f(x)$ is continuous on $[a, b]$ and differentiable on $(a, b)$, and $f(a) = f(b)$, which theorem guarantees the existence of a number $c$ in $(a, b)$ such that $f'(c) = 0$?

The position of a moving object is given by the function $s(t) = 2t^3 - 9t^2 + 12t$, where $s(t)$ represents the position at time $t$. Calculate the average rate of change of the position from $t = 1$ to $t = 3$.

Which expression represents the left-hand limit of $g(x)$ at the point where $x=c$?