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

Question

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.

anonymous · Answer

attachment

anonymous · Answer

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.

goformit100 · Answer

As its a critical graph the reading are very difficult to be talkne out.