Calculus Finals Review (MC) Fall 2024

Front

What is the formula for the volume of a sphere?

Back

V = (4/3)πr³, where r is the radius.

Front

How do you find the rate of change of the volume of a sphere with respect to its radius?

Back

Use the formula dV/dr = 4πr².

Front

What does it mean for a function to be concave down?

Back

A function is concave down if its second derivative is negative, indicating that the slope of the tangent line is decreasing.

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

How do you calculate average velocity over an interval?

Back

Average velocity = (s(b) - s(a)) / (b - a), where s(t) is the position function.

Front

What is a local maximum?

Back

A local maximum is a point where the function value is higher than the values of the function at nearby points.

Front

What is a local minimum?

Back

A local minimum is a point where the function value is lower than the values of the function at nearby points.

Front

What does the first derivative test tell us about a function?

Back

The first derivative test helps determine where a function is increasing or decreasing and identifies local extrema.

Front

What is the significance of the second derivative?

Back

The second derivative indicates the concavity of the function and can help identify points of inflection.

Front

How do you find the derivative of f(x) = 12 - 8x?

Back

f'(x) = -8.