Derivative Graphs Worksheet
Explore the relationship between functions and their derivatives graphically with this Grade 10 calculus worksheet.
Includes
Standards
Derivative Graphs: Grade 10 Calculus
Name:
Date:
Score:
Read each question carefully and provide your answers. For questions involving graphs, analyze the given graph or sketch your own as instructed.
1. If a function's derivative is positive over an interval, what does this tell you about the original function's behavior in that interval?
2. When the derivative of a function is zero at a point, what does this typically indicate about the original function's graph at that point?
3. Consider a function f(x) whose graph is increasing, then reaches a local maximum, and then decreases. Which of the following best describes the graph of its derivative, f'(x)?
f'(x) is always positive.
f'(x) is always negative.
f'(x) starts positive, crosses the x-axis, then becomes negative.
f'(x) starts negative, crosses the x-axis, then becomes positive.
4. If a function f(x) has a sharp corner, its derivative f'(x) will be undefined at that point.
True
False
5. The graph of a derivative f'(x) shows the slope of the tangent line to the original function f(x) at each point.
True
False
6. For the function f(x) shown below, sketch the graph of its derivative, f'(x), on the provided coordinate plane.
To the left is the graph of f(x) = x^3 - 3x. To the right, sketch the graph of f'(x).
7. If the graph of f'(x) is a horizontal line above the x-axis, what can you conclude about the original function f(x)?
Related Worksheets
Squeeze Theorem Practice
A worksheet for Grade 10 students to practice applying the Squeeze Theorem to determine limits of functions.
Derivative by Definition Worksheet
Understand and apply the definition of the derivative to calculate derivatives of various functions.
Implicit Differentiation Worksheet
A Grade 10 Calculus worksheet on implicit differentiation, covering finding derivatives of implicitly defined functions.
Curve Sketching Mastery
This worksheet provides exercises on curve sketching, focusing on identifying key features of functions and their graphs, suitable for Grade 10 Calculus students.
Extrema on a Graph: Calculus Worksheet
Explore the concepts of relative and absolute extrema of functions using graphical analysis for Grade 10 Calculus students.
First Derivative Test Worksheet
A worksheet for Grade 10 students covering the First Derivative Test, including finding critical points, intervals of increase and decrease, and local extrema.
Taylor Series Exploration
This worksheet introduces Grade 10 students to the concept of Taylor series, focusing on understanding polynomial approximations of functions.
Riemann Sums Worksheet
Explore the concept of Riemann sums to approximate the area under a curve, including left, right, and midpoint sums.