g'(x)
Definition
The derivative of a function g(x) represents the rate at which the function is changing at any given point. It measures the slope of the tangent line to the graph of g(x) at that point.
Analogy
Think of driving a car on a curvy road. The derivative, g'(x), tells you how fast your speed is changing as you navigate through different points on the road. If g'(x) is positive, it means you're accelerating; if it's negative, you're decelerating.
Related terms
Derivative: The derivative of a function measures its rate of change or slope at any given point.
Tangent Line: A line that touches a curve at only one point and has the same slope as that point on the curve.
Rate of Change: How much one quantity changes with respect to another quantity. In calculus, this is often represented by derivatives.
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Study guides (1)
Practice Questions (1)
- While driving his truck, David uses up gasoline. If g(x) is the amount of gasoline left in his truck after driving x miles, what is the sign of the first derivative, g'(x)?
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