Question

Will rate, please help!!!

- Use the First Derivative Test to find a) the intervals over which f(x) is increasing and decreasing, and b) the local extrema (mins and maxes) of FC). Write your answers as intervals and ordered pairs. You must show your work to receive credit; simply writing the answer will indicate that you used technology and will not be counted as a valid attempt. Hint: Drawing and labelling a number line is useful. f(x) = x + (a) Increasing: Decreasing: (b) Local Min(s): Local Max(es) (c) Use the second derivative to find the point(s) of inflection of f(x). Write your answer as an ordered pair; you must show your work to receive credit.

Answer 1

fors = 122 - 2 1 f'x> 4x3x? - 3 x 9 +0 = **-3n = X(4-3) for function to be increasing fresto > n(n-3))0 : xoo and (4-3) > >0, and >3. - (3,) x<0 and 23.10. E não and a43 P , 0) for fiuction to be decreasing kiss no -> *123) in so and (2-3) 20 x>0 and a <3 a (0,3) © for local entremas plaszo al1-3)=0 - 3 = 0,3 m - P11%) = 2323 at azo fl120)=-340 Hence at a=0 maxime existe ' f20) = 468392 caj*+{= = maxima at x=3, "(3) = 2x3-3=330 Hence at x=3 mu'n'ma caints $13)» £139-213)*+<> 9-+3 = 2minima for point of inflection ficato a 24-3=0 = *= 3, 41%)" (%)?-313)*+F =0.8125? @ Increasing (oooo) and (3,00) . decreasing (0,3). maxima atx=0 and maximum value = 5% Minima at H=3 and minimum value = -2 © point of inflection (3/2, 0.0125)