Math Flashcards
What is the definition of a derivative?
The slope of the tangent line of a function
The derivative refers to the rate of change.
How do you find the slope of the tangent line for a given function at a point?
Find the derivative of the function and substitute the x-coordinate to get the slope (y-y1=m(x-x1))
This is a key step in finding the tangent line equation.
What is the standard form formula used to find the y-intercept of a tangent line?
y-y1=m(x-x1)
The final formula for the tangent line is derived from this step.
When the tangent line is parallel to another line, what must be true about their slopes?
The slopes must be equal
This applies when finding the tangent line parallel to a given line.
When the tangent line is perpendicular to another line, how can you determine the slope?
The slope of the tangent line is the negative reciprocal of the given line’s slope
This relationship is crucial for finding perpendicular lines.
List the basic rules of derivation.
- Constant
- Power
- Constant multiple
- Sum
- Product
- Quotient
- Chain
- Exponential
Logarithmic and trigonometric rules might also be included.
What is the implicit derivation format for a function with respect to a variable?
Use the format dy/dx
This is used for deriving functions that involve more than one variable.
What does the rate of change refer to in geometry?
It refers to the derivative of a function
This concept is essential for understanding motion and change.
How do you find the instantaneous velocity of an object?
Derive the function that describes the object’s distance over time
This gives the slope and thus the instantaneous velocity.
Fill in the blank: The derivative is usually shown as _______.
f’, Dx, y’, d/dx, and dy/dx
Alternative notations exist for derivatives.
True or False: The rate of change can be expressed using the chain rule.
True
The chain rule is a fundamental concept in calculus.
