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Question: Find (i) x - intercepts, (ii) y - intercept and (iii) critical numbers for the function f(x) = 9-x2?


A ) (i) (- 3, 0), (3, 0); (ii) (0, 3); (iii) x = 0
B ) (i) (- 3, 0), (3, 0); (ii) (0, 3); (iii) x = 1
C ) (i) (9, 0); (ii) (0, 3); (iii) x = 0
D ) (i)(- 3, 0), (3, 0); (ii) (0, - 3); (iii) x = 0
E ) (i) (- 1, 0), (1, 0); (ii) (0, 3); (iii) x = 0

Steps to derive

1 f(x) = 9-x2
 [Write the function.]

2 9-x2 = 0 x = ± 3
x - intercepts are (- 3, 0), (3, 0)
 [Equate f(x) to zero to find x - intercepts and solve for x.]

3 f(0) = 3, so y - intercept is (0, 3)
 [Put x = 0 in f(x) to find y - intercept.]

4 f ′(x) = - x9-x2
 [Find f ′(x).]

5 - x9-x2 = 0 x = 0
Critical number is x = 0
 [Equate f ′(x) = 0 to find critical numbers.]

6 Therefore, the x - intercepts are (- 3, 0), (3, 0), y - intercept is (0, 3) and critical number is x = 0.



Hence the right answer is Option A

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