Calculus Unit 3 Review

Front

What is the derivative of a function?

Back

The derivative of a function measures how the function's output value changes as its input value changes. It represents the slope of the tangent line to the graph of the function at a given point.

Front

What is the product rule in differentiation?

Back

The product rule states that if you have two functions u(x) and v(x), the derivative of their product is given by: (uv)' = u'v + uv'.

Front

What is the chain rule in differentiation?

Back

The chain rule is used to differentiate composite functions. If y = f(g(x)), then the derivative is: dy/dx = f'(g(x)) * g'(x).

Front

How do you find dy/dx for implicit functions?

Back

To find dy/dx for implicit functions, differentiate both sides of the equation with respect to x, treating y as a function of x, and then solve for dy/dx.

Front

What is the significance of critical points in calculus?

Back

Critical points are where the derivative is zero or undefined. They are important for finding local maxima and minima of functions.

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing where its derivative is positive and decreasing where its derivative is negative.

Front

What is the second derivative test?

Back

The second derivative test is used to determine the concavity of a function. If f''(x) > 0, the function is concave up; if f''(x) < 0, it is concave down.

Front

What is the formula for the derivative of sin(x)?

Back

The derivative of sin(x) is cos(x).

Front

What is the formula for the derivative of cos(x)?

Back

The derivative of cos(x) is -sin(x).

Front

What is the power rule in differentiation?

Back

The power rule states that if f(x) = x^n, then f'(x) = n*x^(n-1).