Differential Equations

The rate of change of a quantity A is directly proportional to the square of A and inversely proportional to the time t. Which of the following differential equations represents this situation?

If a function $f(x)$ is differentiable at $x = a$, which of the following must be true about $f$ at $x = a$?

Which type of test gives information on whether a critical point is a local maximum or minimum for a differentiable function?

If a differential equation $\frac{dy}{dx} = ky$ represents exponential growth, what must be true about $k$?

The amount of money in a savings account is given by the function A(t), where t is measured in years and A is measured in dollars. The rate of change of money is proportional to the square root of the current amount of money. When the account contains 10,000, the amount of money is increasing at 1,000/year. What is t...

The acceleration of a racing car is proportional to the position of the car times the time passed. After 2 seconds, the car has traveled 12 meters and the acceleration is 6 meters per second per second. If x(t) is the position of the car, what is the differential equation that represents the situation?

t seconds after a Calculus textbook is dropped from a building, the rate of change of the textbook’s position is proportional to the amount of time passed. If y(t) is the position of the textbook at time t, which of the following differential equations represents this situation?

Given that $\frac{dy}{dx} = y \ln(y)$ for all real numbers where both sides are defined, what can be concluded about the graph of the differential equation's solutions?

If a cup of coffee cools according to Newton's Law of Cooling, which differential equation models the temperature change over time if $T$ is the temperature of the coffee and $T_r$ is the room temperature?

Given that a particle moves along a line so that its velocity at time t is given by $v(t)=3t^{2}-6t+5$, for what intervals of time t does it accumulate distance?