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Bladerunner1122
1. Let g be the function given by g(x)=integrate from -4 to x f(t)dt. For each of g(-1), g'(-1), and g''(-1), find the value of state that it does not exist. 2. For the function g defined in part 1., find the x-coordinate of each point of inflection of the graph of g on the open interval -4<x<3. Explain your reasoning. 3. Let h be the function given by h(x)= integrate from x to 3 f(t)dt. Find all values of x in the closed interval -4≤x≤3 for which h(x)=0. 4. For the function h defined in part 3, find all intervals on which h is decreasing. Explain your reasoning.
step 1) from graph, f(x) is a piecewise linear function. and hence, g(x) is piecewise quadratic step 2) g(x) is quadratic and continuous derivative exists step 3) g'(x) will be piecewise linear and continuous step 4) g''(x) will be constant terms in each interval and discontinuous at the change of domains. hence, g''(-1) cannot exist.
As its a critical graph the reading are very difficult to be talkne out.