Problem 1
Describe what an "extreme value" of a function is in your own words.
Problem 1
Why is sketching curves by hand beneficial even though technology is ubiquitous?
Problem 1
In your own words describe what it means for a function to be increasing.
Problem 1
Sketch a graph of a function \(f(x)\) that is concave up on \((0,\) and is concave down on (1,2) .
Problem 2
What does a decreasing function "look like"?
Problem 2
Explain in your own words what Rolle's Theorem states.
Problem 2
Sketch a graph of a function \(f(x)\) that is: (a) Increasing, concave up on (0,1) , (b) increasing, concave down on (1,2) , (c) decreasing, concave down on (2,3) and (d) increasing, concave down on (3,4) .
Problem 2
What does "ubiquitous" mean?
Problem 3
A function \(f(x)\) and interval \([a, b]\) are given. Check if Rolle's Theorem can be applied to fon \([a, b] ;\) if so, find cin \([a, b]\) such that \(f^{\prime}(c)=0\). \(f(x)=6\) on [-1,1] .
Problem 3
Is is possible for a function to be increasing and concave down on \((0, \infty)\) with a horizontal asymptote of \(y=1 ?\) If so, give a sketch of such a function.
