1. What is the connection between critical numbers and relative extrema? 2. What
ID: 3343676 • Letter: 1
Question
1. What is the connection between critical numbers and relative extrema?
2. What are inflection points? How do you find them?
3. Determine whether the following statement is true or false. Whether true or false, explain why. If false, also correct the statement.
If f '(c) < 0, then f is concave down at x = c.
4. Determine whether the following statement is true or false. Whether true or false, explain why. If false, also correct the statement.
If f "(x) < 0, for all real numbers x, then f decreases without bound.
Explanation / Answer
1)critical numbers are those numbers wher the derivative is 0.
But relative extrema are those points where first derivative is zero along as second dervative is less than 0.
2)Inflection points are those points where the graph changes from concave to convex or vice.
Those points whose first and second derivative are 0 are called as inflection points.
3)FALSE
f'(c)<0 just implies the the slope of the graph at that point is negetive i.e decreasing
4)
FALSE
f''(c)<0 for all real numbers implies that the curve is cancave upwards.
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