Functions and Limits
If f(x) = 2x - 5, this is when f(x) = 10.
What is when x = 7.5 or 15/2?
Draw and label examples of a jump discontinuity, as asymptote, and a hole.
What is [answers will vary - Mr. Lester will judge]?
This is the derivative of sin(x).
What is cos(x)?
This is the derivative of sin(ex).
What is cos(ex)ex?
These are the names of Mr. Lester's cats.
What are Kenai and Luna?
This is the slope of a line passing through the points (3, 5) and (7, -2).
What is -7/4 or -1.75?
Draw a picture exemplifying how the squeeze theorem can be used to prove facts about limits of functions squeezed between other functions.
What is [answers will vary - Mr. Lester will judge]?
This is the derivative of ln(x).
What is 1/x?
This is the derivative of (x2 - 10x)/(ln(x)).
What is [this is really hard to type on the jeopardy board without paying for the subscription -- I will just tell you if it is right]?
The Mean Value theorem states that if f(x) is continuous on [a,b] and ______________ on (a,b), the ___________ rate of change at some point x=c, a<c<b, equals the __________________ rate of change over the whole interval [a,b]. Fill in all three blanks.
What is differentiable, instantaneous, average?
This is the limit as x ---> 3 of g(x) = 0.5x - 10.
What is -8.5 or -17/2?
Does the function f(x) = 3x2 + 10x - 17 have a zero on the interval [1, 4]? Justify your answer.
What is yes, f(1) = -4 and f(4) = 61, and -4 < 0 < 61 and f(x) is continuous so the IVT guarantees a zero on [1,4]. (Or at least the spirit of this answer)
This is the derivative of 3x3 - 10x + 17.
What is 9x2 - 10?
This/these are the critical number(s) of f(x) = x2 - 6x + 8.
What is x = 3?
This is the second derivative of position.
What is acceleration?
This is the limit as x ---> 2 of (x2 + 4x - 12)/(x-2).
What is 8?
These are the two main interpretations of what a derivative tells us.
What are instantaneous rates of changes and slopes of tangent lines?
This is the derivative of x3cos(x).
What is 3x2cos(x) - x3sin(x)?
These are the interval(s) on which f(x) = (1/3)x3 - 6x2 - 45x + 291 is increasing.
What are ( -infinity, -3) and (15, infinity)?
This is Mr. Lester's wife's name.
What is Savannah?
This is the limit as x ---> 25 of (sqrt(x) - 5)/(x-25).
What is 1/10?
Write down the limit definition of a derivative for a function f(x).
What is (the limit as h --> 0) (f(x+h)-f(x))/h?
This is the slope of the tangent line to the graph of 4x2ex at the point x = 0.
What is 0?
Find the absolute maximum and minimum of the function g(x) = 4x3 + 6x2 on the interval [-2, 0.5].
What is that the absolute maximum is 2 and the absolute minimum is -8?
This is what you should do if Mr. Lester gives you a problem about a bug with a given position function and asks you its speed at a certain time.
What is take the derivative and plug in that number?