Fall 2025 Math 65A Study Guide for Test #3

The flashcards cover key concepts and terminology relevant to sections 4.4 to 7.3 of the course, which are important for preparing for Test #3.

Second-Derivative Test

A method to find relative maxima and minima of a function by analyzing the sign of the second derivative.

Relative Maximum

A point on the graph of a function where the function value is greater than or equal to the function values in its immediate vicinity.

Relative Minimum

A point on the graph of a function where the function value is less than or equal to the function values in its immediate vicinity.

Critical Points

Points on the graph of a function where the derivative is zero or undefined, possibly indicating local maxima or minima.

Optimization Problems

Problems that involve finding the maximum or minimum value of a function subject to certain constraints.

Newton's Method

An iterative numerical method for finding successively better approximations to the roots (or zeros) of a real-valued function.

Antiderivative

A function whose derivative is the given function; also known as an indefinite integral.

Riemann Sum

A method for approximating the total area under a curve by dividing it into subintervals and summing the areas of rectangles.

Fundamental Theorem of Calculus

Links the concept of differentiation and integration, stating that the derivative of the integral of a function is the original function.

Concavity

The property of a curve that describes whether it is curving upwards or downwards, often analyzed using the second derivative.

Inflection Point

A point on the curve where the concavity changes, determined by where the second derivative changes sign.

Local Extrema

Points on a graph where the function has locally maximum or minimum values.

Area Under Curve

The number of square units between the curve and the x-axis over a given interval, often found using definite integrals.

Max-Min Integral Inequality

A rule to find upper and lower bounds for integrals by comparing values within specified ranges.

Volume of Revolution

The volume of a solid obtained by rotating a curve around an axis.