Local extrema: peaks and valleys in a specific region. Global extrema: absolute highest and lowest points of the entire graph.

Zeros: x-values where $f(x) = 0$. Critical points: x-values where $f'(x) = 0$ or $f'(x)$ is undefined.

Even: ends point in the same direction. Odd: ends point in opposite directions.

Root: where the graph intersects the x-axis. Turning point: local max or min.

Increasing: the function's value goes up as x increases. Decreasing: the function's value goes down as x increases.

Concavity: describes the curve's bend (up or down). Slope: describes the steepness and direction of the line tangent to the curve.

Zero: point where the graph crosses the x-axis. Inflection point: point where the concavity changes.

First derivative: gives the rate of change of the function. Second derivative: gives the rate of change of the first derivative (concavity).

Local maximum: the highest point in a specific region. Global maximum: the highest point on the entire graph.

Critical point: point where the derivative is zero or undefined. Endpoint: a point at the boundary of the function's domain.

A function of the form $p(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$, where 'n' is a non-negative integer and the 'a' values are real numbers.

The highest power of the variable in the polynomial.

A point on the graph of a function that is a peak within a specific region.

A point on the graph of a function that is a valley within a specific region.

The absolute highest point of the entire graph of a function.

The absolute lowest point of the entire graph of a function.

The x-values where the function crosses the x-axis (where $f(x) = 0$).

A point on a curve where the concavity changes (from concave up to concave down, or vice versa).

The coefficient of the term with the highest power in a polynomial.

The direction in which a curve bends. It can be concave up or concave down.

1. Set $p(x) = 0$. 2. Factor the polynomial. 3. Solve for x.

1. Find the derivative $p'(x)$. 2. Set $p'(x) = 0$. 3. Solve for x.

1. Find critical points. 2. Create a number line with critical points. 3. Test values in each interval in $p'(x)$.

1. Find critical points. 2. Use the first or second derivative test to determine if each point is a local max, min, or neither.

1. Find zeros. 2. Find extrema. 3. Determine end behavior. 4. Plot these points and sketch the curve.

1. Identify the leading term ($a_nx^n$). 2. If n is even and $a_n > 0$, both ends go to $+\infty$. 3. If n is even and $a_n < 0$, both ends go to $-\infty$. 4. If n is odd and $a_n > 0$, left goes to $-\infty$, right goes to $+\infty$. 5. If n is odd and $a_n < 0$, left goes to $+\infty$, right goes to $-\infty$.

1. Find the second derivative $p''(x)$. 2. Set $p''(x) = 0$ and solve for x. 3. Check that the concavity changes at these points.

1. Find the second derivative $p''(x)$. 2. Determine intervals where $p''(x) > 0$ (concave up) and $p''(x) < 0$ (concave down).

1. Set $p(x) = y$. 2. Solve for x.

1. Check the end behavior. 2. If the end behavior approaches infinity, there is no global max/min. 3. If the end behavior approaches a finite value, check for local max/min and compare.