Question 13:The graph of g' is shown here. Which of the following statements is (are) true of g?I. g is continuous at x = aII. g is differentiable at x = aIII. g is increasing in an interval containing x = a(A) I only(B) III only(C) I and III only(D) II and III only(E) I, II, and III
Question
Question 13:The graph of g' is shown here. Which of the following statements is (are) true of g?I. g is continuous at x = aII. g is differentiable at x = aIII. g is increasing in an interval containing x = a(A) I only(B) III only(C) I and III only(D) II and III only(E) I, II, and III
Solution
Without the graph, it's impossible to accurately answer this question. However, I can explain what each statement means:
I. g is continuous at x = a: This means that the function g does not have any holes, jumps, or asymptotes at x = a.
II. g is differentiable at x = a: This means that the function g has a defined slope at x = a. In other words, it's possible to draw a tangent line to the curve of the function at this point.
III. g is increasing in an interval containing x = a: This means that the values of the function g are getting larger as x moves from left to right in an interval that contains x = a.
Depending on the graph of g', different combinations of these statements could be true.
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