Podcast
Questions and Answers
What does the gradient of an equation represent?
What does the gradient of an equation represent?
- x/y
- dy/dx (correct)
- y/x
- dx/dy
What does it mean to differentiate a function?
What does it mean to differentiate a function?
dy/dx
What does the gradient of a tangent or function indicate?
What does the gradient of a tangent or function indicate?
- 0
- dy/dx (correct)
- dx/dy
- y/x
What does it mean to find the derivative?
What does it mean to find the derivative?
What indicates an increasing function?
What indicates an increasing function?
What indicates a decreasing function?
What indicates a decreasing function?
Flashcards
Gradient of an equation
Gradient of an equation
Represents the rate of change of a quantity with respect to another quantity, specifically dy/dx for functions of x.
Differentiate a function
Differentiate a function
Calculate the rate of change-- or slope of the tangent line-- of a function with respect to a variable, often dy/dx.
Gradient of a tangent
Gradient of a tangent
The instantaneous rate of change or slope of a function's tangent line at a specific point on the graph.
Find the derivative
Find the derivative
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Increasing function
Increasing function
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Decreasing function
Decreasing function
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Study Notes
Gradient and Derivatives
- The gradient of an equation is represented by the notation dy/dx, indicating the slope at any given point on the curve.
- Differentiation is the process of finding the derivative of a function, also denoted as dy/dx.
- The gradient of a tangent line to a curve at a specific point is determined by dy/dx, reflecting the function's behavior at that point.
- To find the derivative of a function means to calculate dy/dx, providing essential information for analysis of the function.
Function Behavior
- An increasing function is characterized by a positive gradient, indicated by dy/dx > 0, meaning as x increases, y also increases.
- A decreasing function is one where the gradient is negative, denoted by dy/dx < 0, indicating that as x increases, y decreases.
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Description
Test your understanding of key concepts in GCSE Further Maths with these flashcards. Covering topics like differentiation, gradients, and increasing or decreasing functions, this resource is essential for mastering the subject. Perfect for quick revision or study sessions.
