The graph of f is shown in the figure.X =ti(a) For which values of x is f'(x) zero? (Enter your answers as a comma-separated list.)2xFor which values of x is f'(x) positive? (Enter your answer using interval notation.)For which values of x is f'(x) negative? (Enter your answer using interval notation.)What do these values mean?f is --Select--when f'> 0 and fis --Select--- when f' < 0.X =(b) For which values of x is f"(x) zero? (Enter your answers as a comma-separated list.)For which values of x is f"(x) positive? (Enter your answer using interval notation.)For which values of x is f"(x) negative? (Enter your answer using interval notation.)What do these values mean?fis---Select--X =◆ when f"> 0 and fis --Select---(c) On what open interval is f' an increasing function?(d) For which value of x is f'(x) minimum?when f" < 0.For this value of x, how does the rate of change of f compare with the rates of change of f for other values of x?Explain.The rate of change of f at this value of x is -Select-- the rate of change of f for all other values of x.

Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and specify the other subparts (up to 3) you’d like answered.a) f'(x) is zero at the critical points. At x=-2 and x=2 the graph took turn. So they are critical points. There f'(x)=0Answer: -2, 2 f'(x) is positive when f(x) is increasing. In the intervals (-∞, -2) and (2, ∞) f(x) is increasing. So there f'(x)>0Answer: (-∞, -2) , (2, ∞) f'(x) is negative when f(x) is decreasing. In the interval (-2,2), f(x) is decreasing. So there f'(x)<0Answer: (-2, 2)f is increasingwhen f'<0.f"(x)=0 when function concavity changes f"(x)=0 when x=0f"(x) is positive when concave upward. f"(x) is positive in the interval f"(x) is negative when concave downwardf"(x) is negative in the interval f is concave up when f">0 and f is concave down when f"<0.f'(x) increasing when f"(x) >0f' increasing in the interval:Answer: