Learning Outcomes
- Apply basic derivative rules
- Use the product rule for finding the derivative of a product of functions
- Use the quotient rule for finding the derivative of a quotient of functions
- Apply the chain rule together with the power and product rule
- Write function equations using given conditions
In the Motion in Space section, we will explore motion along plane and space curves. Here we will review properties for taking derivatives and how to write function equations using given conditions.
Basic Derivative Rules
(See Module 3, Skills Review for Calculus of Vector-Valued Functions)
The Product Rule
(See Module 3, Skills Review for Calculus of Vector-Valued Functions)
The Quotient Rule
(See Module 3, Skills Review for Calculus of Vector-Valued Functions)
The Chain Rule
(See Module 3, Skills Review for Calculus of Vector-Valued Functions)
Write Function Equations Using Given Conditions
Sometimes, to find a missing value in a function equation, you will be given an input of the function and the corresponding output. You will then plug this input and output into the function equation and find the missing value.
Example: Writing a Function Equation from given conditions
Given [latex]f(2)=-1[/latex], find the unknown value c in the function equation [latex]f(x)=3x^3-4x^2-x+c[/latex].
Try It
Given [latex]f(1)=5[/latex], find the unknown value c in the function equation [latex]f(x)=-2x^2+3x+c[/latex].
