Chapter 4 | Applications of Derivatives
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4.5 EXERCISES 194. If c is a critical point of f ( x ), when is there no local maximum or minimum at c ? Explain. 195. For the function y = x 3 , is x =0 both an inflection point and a local maximum/minimum? 196. For the function y = x 3 , is x =0 an inflection point? 197. Is it possible for a point c to be both an inflection point and a local extrema of a twice differentiable function? 198. Why do you need continuity for the first derivative test? Come up with an example. 199. Explain whether a concave-down function has to cross y =0 for some value of x . 200. Explain whether a polynomial of degree 2 can have an inflection point. For the following exercises, analyze the graphs of f ′, then list all intervals where f is increasing or decreasing.
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