True/False? If f f is concave down ‘(x) < 0 then If f = 0 then f has an inflection point at x. ‘’(x) If f = 0 then f could have a maximum, or a minimum, or neither ‘(x) If f is differentiable then f must be continuous If f = 0 or f is undefined, then x is called critical point ‘(x) ‘(x) If x=c is a critical point for f, then f must have a relative extrema at x=c Picture Problems: Consider the graph of a function as shown: In the coordinate system below you can see the graphs of and its derivative Who is the f(x) f ’(x). function, who is the derivative? For the graph shown below, draw the derivative f as best as you can. ‘(x) 5. For the function displayed below, find the following limits and derivatives: a) = 2 b) f = 0 ‘(0) c) = 2 d) f negative ‘’(0) e) = + infty f) f negative ‘(10)
True/False? If f ‘(x) < 0 then f is concave down If f ‘’(x) = 0 then f has an inflection point at x. If f ‘(x) = 0 then f could have a maximum, or a minimum, or neither If f is differentiable then f must be continuous If f ‘(x) = 0 or f ‘(x) is undefined, then x is called critical point If x=c is a critical point for f, then f must have a relative extrema at x=c Picture Problems: Consider the graph of a function as shown: In the coordinate system below you can see the graphs of f(x) and its derivative f ’(x). Who is the function, who is the derivative? For the graph shown below, draw the derivative f ‘(x) as best as you can. 5. For the function displayed below, find the following limits and derivatives: a) = 2 b) f ‘(0) = 0 c) = 2 d) f ‘’(0) negative e) = + infty f) f ‘(10) negative