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# Find the open intervals where the function is concave upward or concave downward. Find any inflection points. f(x)=-(x+1)6 Find any critical numbers for f

## Find the open intervals where the function is concave upward or concave downward. Find any inflection points. f(x)=-(x+1)6 Find any critical numbers for f and then use the second derivative test to decide whether the critical number(s) lead to relative maxima or relative minima. If f''(c) = 0 or f''(c) does not exist for a critical number c, then the second derivative test gives no information. In this case, use the first derivative test instead. f(x)=4x-10x+9 Complete parts (a) through (c) for the following function. f(x)=x -30x+29 (a) Find intervals where the function is increasing or decreasing, and determine any relative extrema. (b) Find intervals where the function is concave upward or concave downward, and determine any inflection points. (c) Graph the function, considering the domain, critical points, symmetry, relative extrema, regions where the function is increasing or decreasing, inflection points, regions where the function is concave upward or concave downward, intercepts where possible, and asymptotes where applicable. Sketch the graph of a single function that has all of the properties listed. a. Continuous and differentiable for all real numbers b. f'(x)>0 on (co, -2) and (2,6) c. f'(x) 0 on (1,4) f. f'(-2)=f'(6)=0 g. f'(x)=0 at (1,3) and (4,4) Choose the correct graph below. O A. OB. C. G O D.

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