Question

Question 11 10 pts The derivative f'(2) of an unknown function f(x) has been determined as f'(x) = (x - 2)(+3)2. Use this derivative to find the intervals where the original function f is increasing/decreasing. Then find the x-values that correspond to any relative maximums or relative minimums of the original unknown function f(x). O no relative maximum; relative minimum at x=2 relative maximum at x=-3; no relative minimum O relative maximum at x=2; relative minimum at x=-3 relative maximum at x=-3; relative minimum at x=2 relative maximum at x=2; no relative minimum

Answer 1

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(P-1) Sinee f'w = (x-2) (x+3) f"(= (1-2) 21013) +(ars)? To find Critical Point we have to f'(x) = 6 -) 6e-2) (243) 50 * De-2=0 /(1+3)=0 H=2 243=0 75-3 atx=2, f (2) = 52go so min Value at a=2 at 12-3, f (+3) = 0, so Does not concluse ony decimin So, So No relative maximus :relative minimuss at 2=2 (Q-12) Clearly from the graph we can say that Concave up on (-2,-5) 0 (-2,2) and Concare down. (-5,-2) 0 (2,A), a values of infleetio points 93-5,23-2,8=2