Question

1. (1 point) Let f(x) = -3 - 9x? +152 +5. Find the open intervals on which is increasing (decreasing). Then determine the 2-coordinates of all relative maxima (minima). f is increasing on the intervals f is decreasing on the intervals 3. The relative maxima of foccur at 2 = 4. The relative minima off occur at - 2. Notes: In the first two your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word "none" In the last two your answer should be a comma separated list of values or the word "none".

Answer 1

f'(a) 7,0 f(x) = x² ga+15%+5. fis Continuous and differentiable. f'(x) = 3 2 -18x + 15 = 3 (**-62+5) = 3(2-5)(-1). f is increasing if Either 1-5>0,X-1), o 3(2-5) (a-D 70. (2-5) <o, (-1) SO. → Either 27,5 6ie. The open intervals where f is increasing | (-0, 1) and 5,0 o similarly f is decreas reasing if f (x) so. → 6-5) (2-1) So =) 15 a 25 Hence the open interval where f is decreasing is [C1,5) test local extremas by zad derivative test that f"G) 3 (22-6) = 6 (2-3) Local extremas those points where f(a) ao ie are (3) we'll Note 1-1,5

Now the © Since f" (1) = 6(1-3) =-12 <0, relative maxima maxina of f occurs at all since f" (5) f" (5) = 665-3) = 12 %0,, The relative minima occurs at 2-5 of f