Differentiation: Definition & Rules unit test
A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.
Alternate form of the definition
Tangent vs normal line
Using a tangent line to approximate
Higher-order derivatives
Recognizing a limit as a derivative
Derivative as a limit
Product rule
Derivatives of trig functions
Derivative as slope of the tangent
Differentiability implies continuity
Derivative from a table of values
Where a function fails to be differentiable
Short answer 1. Define or explain: Quotient rule
3 ptsShort answer 2. Define or explain: Power rule
3 ptsShort answer 3. Define or explain: Derivative of aˣ and log_a x
3 ptsShort answer 4. Define or explain: Derivative of eˣ and ln x
3 ptsFree response
9 ptsThis course has no free-response prompt tagged to this unit, so one from elsewhere in the course is used. It is still worth writing — the skill transfers.
Consider the differential equation dy/dx = xy², and let y = f(x) be the particular solution with f(0) = 1.
Write an equation for the line tangent to the graph of f at (0, 1), and use it to approximate f(0.5).
Use separation of variables to find the particular solution y = f(x).
State the largest open interval containing x = 0 on which the solution from part (b) is defined, and explain what limits it.