math quiz 11 & 12
11 An absolute maximum point is also a relative maximum point
false
11 If we sketch the graph of the function f(x)=(x−1)2 on its entire domain (−∞,∞), it has a relative maximum point
false
11 If we sketch the graph of the function f(x)=(x−1)2 on its entire domain (−∞,∞), it has no relative minimum point
false
11 If we sketch the graph of the function f(x)=ex on its entire domain (−∞,∞), it has a relative maximum point, but no relative minimum point
false
11 Not all functions have absolute extrema, but all functions have relative extrema.
false
12 Relative maximum and minimum points for the graph of a function can occur at some point which is not one of the critical numbers for the function.
false
11 An absolute maximum point may not be a relative maximum point
true
11 An absolute minimum point may not be a relative minimum point
true
11 I The graph of a function changes from rising to falling at a relative maximum point.
true
12 If the graph of f″(x) lies on the x-axis, then the graph of f(x) could have a inflection point.
true
12 If the values of f″(x) are negative, then the graph of f(x) is concave down.
true
12 Relative maximum and minimum points for the graph of a function can only occur at the critical numbers for the function.
true
11 Relative extrema can occur at any point of a graph, even the endpoints.
false
12 If f′(c)=0 for some function f(x)), then the graph of f(x) has a relative maximum point if f″(c)>0.
false
12 If f′(c)=0 for some function f(x), then the graph of f(x) has a relative minimum point if f″(c)<0.
false
12 If the graph of f″(x) is below the x-axis, then the graph of f(x) is concave up.
false
12 If the graph of f″(x) lies on the x-axis, then the graph of f(x) must have an inflection point.
false
12 If the values of f″(x) are positive, then the graph of f(x) is concave down.
false
11 If the point P is the highest point on the graph of y=f(x), then P must be an absolute maximum point for the graph.
true
11 If the point P is the lowest point on the graph of y=f(x), then P must be an absolute minimum point for the graph.
true
11 If we sketch the graph of the function f(x)=(x−1)2 on its entire domain (−∞,∞), it has a relative minimum point
true
11 If we sketch the graph of the function f(x)=(x−1)2 on its entire domain (−∞,∞), it has no relative maximum point
true
11 If we sketch the graph of the function f(x)=ex on its entire domain (−∞,∞), it has no relative maximum or minimum points
true
11 Relative extrema cannot occur at an endpoint of a graph.
true
11 The graph of a function changes from falling to rising at a relative minimum point.
true
11 The graph of a function changes from rising to falling at a relative maximum point.
true
12 If f(x)=x3+5, the graph of f(x) has a point of inflection when x=0.
true
12 If f′(c)=0 for some function f(x), then the graph of f(x) has a relative minimum point if f″(c)>0.
true
12 If the graph of f″(x) is above the x-axis, then the graph of f(x) is concave up.
true