Key Vocab
When does a critical point occur?
What is "When f'(x)=0 or is undefined"?
(don't need to say both, one is fine)
If position is s(t), wjat does s'(t) represent?
(v(t) works too)
Why do optimization problems include a restriction (fixed perimeter or fixed area)
What is "to limit the possible solutions so a max or min can be found"?
When is implicit differentiation used?
What is "when y is not isolated"?
x2+y2=10, find dy/dx
What is "dy/dx= -x/y"?
What does it mean if a function is increasing on an interval? (in terms of its first derivitive)
What is "the derivitive is positive on that interval"?
When is a particle at rest?
What is "when velocity equals zero"?
What do you do after taking the derivative in an optimization problem?
What do you include when differentiating in terms with y?
What is "dy/dx"?
A particle's postion is s(t)=t24t, what is the velocity function?
What is "v(t) = “12t^2”?
What does the Second Derivative Test help determine?
What is "Whether a critical point is a local max or min"?
What does acceleration represent? (think derivatives)
What is "the derivative of velocity"?
(v'(t) works as well)
Why do we check critical points in optimization?
What is "they are possible max or min values"?
What rule is used when x & y are multiplied?
What is "the curve is decreasing"?
What is an absolute maximum?
What is "the greatest value of a function on an interval"?
If velocity is negative, what direction is the particle moving?
What is "to the left"?
What test is commonly used to find absolute extrema?
What is "the Candidates Test"?
After implicit differentiation, what do you usally solve for?
What is "dy/dx"?
2x+y2=7, find dy/dx
What is "dy/dx= -1/y"?
What does it mean if the second derivative (f''(x)) is positive? (Mention f'(x) AND f(x))
What is "the first derivative (f'(x)) is increasing and the curve on the graph is concave up"
(Must mention both for full points, mentioning 1 is half points!)
What does speed measure? (speed = ?) (think formula)
What is "the absolute value of velocity"?
(|v(t)| works too)
What type of problems usally involce words like "'argest", "smallest", or "maximum"? (Hint, name of this category lol)
What is "whether the curve is increasing or decreasing"?
x3+y3=6, find dy/dx