Home > CALC > Chapter 3 > Lesson 3.4.1 > Problem 3-153
3-153.
Sketch a continuous curve which meets all the criteria: Homework Help ✎
f ′(x) > 0 for all x
f(x) is concave down.
f(2) = 1
How many roots do f(x) have?
What can you say about the location of the root(s)?
Find
Is it possible that f ′(1) = 1 ?
f'(x) > 0 means f(x) is always increasing.
f(x) looks something like a square root graph (w/out the endpoint) or a logarithmic graph (w/out the asymotote).
If f(2) = 1, then the point (2,1) lies on the graph of the function.
Is it possible for a function that is always increasing (hint 1) AND always concave down (hint 2) to have no roots?
On what domain could the root(s) not exist?
Could there be a horizontal asymptote as x → −∞?
