help with q, r, and \'s please 3. Let F(x)=l\'f(t)dt wherefis the function graph
ID: 2890727 • Letter: H
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help with q, r, and 's please
3. Let F(x)=l'f(t)dt wherefis the function graphed below. F consists oflines and a semi-circle. f(x) Find the following: a. F(0)0 c. F(4): 2 j. F(2) 2 k. F (6) -2 I. F (5) i. F(4) o m. F (2) n. F (5) q. On what subintervals of [-4, 6] is F increasing and decreasing? Justify your answer. r. Find the absolute minimum and maximum values of x on the interval. Justify your answer s. On what subintervals of [-4,6) is F concave up/concave down? What are the inflection points? Justify o, F"(-0.5), ½ P. F(0) your answers.Explanation / Answer
q) F is increasing or decreasing depending upon how its value is changing with a small change in the right direction (small increase) of x-axis;
For [-4,-3] F is decreasing
For [-3, -2] F is increasing
For [-2,-1] F is neither increasing nor decreasing
For [-1,0] F is decreasing
For [0,2] F is increasing
For [2,6] F is decreasing
These conclusions can be seen from the graph itself;
q) From the graph, it can be concluded that
The absolulte maxima of F occurs at x= [-2,-1] U {2) and is : F(absolute maxima) = 2;
The absolulte minima of F occurs at x= {-3} U {6} and is : F(absolute minima) = -2
s) concave up means dropping water increasing graph; Or f''(x) > 0 and f''(x) > 0
concave down means dropping water decreasing; Or f'(x) < 0 and f''(x) > 0
Thus, f is concave up for x=[0,2] and concave down for x= [2,4]
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