Question

Suppose that a continuous function f has a derivative f' whose graph is shown below over the interval (1, 10). y=f'(x) 1 2 3 4 5 6 8 9 10 (a) Find the interval(s) over which f is increasing. (Enter your answer using interval notation.) Find the interval(s) over which fis decreasing. (Enter your answer using interval notation.) (b) Find the x-value(s) where f has a local maximum. (Enter your answers as a comma-separated list.) x = Find the x-value(s) where f has a local minimum. (Enter your answers as a comma-separated list.) X = (c) Find the interval(s) over which fis concave upward. (Enter your answer using interval notation.) Find the interval(s) over which f is concave downward. (Enter your answer using interval notation.) (d) Find the x-value(s) where f has an inflection point. (Enter your answers as a comma-separated list.)

Answer 1

.. by the graph we can see that f (H) co och<2 and 7ereg f(x) > 0 : 2<Hc 7 and g < X <10 fle) = 0 at x=2, 7, and g. @ f is increasing when fixe) > 0 2 x + 3C2, 7) ( 9,49)

& f(x) co f is decreasing when xe (2,20 ( 1 (9) 2 6 - - 6 f. has bocal maxima where f(x) <0 at x = 7 f(x)=0 and f'(sl.co 7 Tx=77 is local maximam. and at a= 2 and a=9 • fin) = 0 and f(x) > Tx = 3 and (x=9 ] are local minimam.

Cencare Concare up = f(x) >O » where f(se) is increasing. ) x (6, 3), (4,6 ) , 8, 9, 1 Concare clown f'(x)co where f'(x) is decreasing → XF (3,4), (6,8) point of inflection f '(x)=0 = (x = 3,4,6,8,