C.FGR.3: : Relate limits and continuity to the derivative as a rate of change and apply it to a variety of situations including modeling contexts.
C.FGR.3.1: : Interpret the derivative as an instantaneous rate of change that is a two-sided limit of an average rate of change.
Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine.
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C.FGR.3.3: : Apply the concept of derivative geometrically, numerically, and analytically.
Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine.
5 Minute Preview
C.FGR.3.5: : Find the derivatives of a variety of relations.
Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine.
5 Minute Preview
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine.
5 Minute Preview
C.FGR: : Functional & Graphical Reasoning – Applications of Differentiationt
C.FGR.4: : Apply derivatives to situations in order to draw conclusions including curve analysis and modeling rates of change in applications.
C.FGR.4.1: : Calculate the slope of a curve at a point.
Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine.
5 Minute Preview
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.
Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine.
5 Minute Preview
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.
Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine.
5 Minute Preview
C.FGR.4.4: : Identify points of inflection and intervals of concavity of a function by using the second derivative of a function.
Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine.
5 Minute Preview
C.FGR.4.5: : Compare characteristics of f, f’, and f” graphically, numerically, analytically, and with technology.
Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine.
5 Minute Preview
C.FGR.4.9: : Model rates of change in applied situations.
Graphs of Derivative Functions
What does the graph of a derivative function look like? What can a derivative function tell you about the original function? What can't it tell you? Explore these questions for five different types of functions: linear, quadratic, cubic, absolute value, and sine.
5 Minute Preview
C.GSR.5: : Analyze the relationship between the derivative and the integral using the Fundamental Theorem of Calculus.
C.GSR.5.1: : Use Riemann sums to approximate values of definite integrals.
Riemann Sum
Approximate the area under a curve in an interval using rectangles. Compare the results of left-hand summation to the results of right-hand summation. Vary the interval and the number of rectangles and explore how the graph of the rectangles and curve change in response.
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Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
