---
title: "C.FGR.4: Derivative Applications Overview (Georgia Mathematics standard)"
code: C.FGR.4
cite_as: Georgia Standards of Excellence, Mathematics, C.FGR.4
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/C.FGR.4
md_url: https://georgiahomeroom.org/standards/code/C.FGR.4.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/C.FGR.4.md
source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180
source_last_changed: 2024-10-09
data_built: 2026-09-18
publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district.
up: https://georgiahomeroom.org/standards/math/high-school.md
index: https://georgiahomeroom.org/standards/index.md
---

# C.FGR.4: Derivative Applications Overview

Apply derivatives to situations in order to draw conclusions including curve analysis and modeling rates of change in applications.

- Subject: Mathematics
- Appears in: High School, https://georgiahomeroom.org/standards/math/high-school.md

## Expectations

- Analyze function behavior using the derivative.
  - **C.FGR.4.1**: Calculate the slope of a curve at a point.
  - **C.FGR.4.2**: Write the equation of the tangent line to a curve at a point and use it to obtain a local linear approximation of a value near the point of tangency.
  - **C.FGR.4.3**: Identify intervals where functions are increasing, decreasing, and constant by using the relationship between the function and the sign of its first derivative.
  - **C.FGR.4.4**: Identify points of inflection and intervals of concavity of a function by using the second derivative of a function.
  - **C.FGR.4.5**: Compare characteristics of f, f’, and f” graphically, numerically, analytically, and with technology.
  - **C.FGR.4.6**: Apply Mean Value Theorem.
- Apply the derivative to real-world problems.
  - **C.FGR.4.7**: Apply Extreme Value Theorem.
  - **C.FGR.4.8**: Apply the derivative to real-world problems to find both local and absolute extrema, with and without technology.
  - **C.FGR.4.9**: Model rates of change in applied situations.

## Georgia Milestones coverage

No Georgia Milestones blueprint cites this standard.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.