Question 8 For each part, draw a sketch of the graph of a function that satisfies each respective condition. (Please draw each part on separate coordinate planes). (a)
f^(')(2)=0
and
f^('')(2)>0
and
f
has a domain of
[-2,\infty )
and
f
has a range of
(-\infty ,5]
. (b)
\lim_(h->0)(f(x+h)-f(x))/(h)=-2
for
\int_0^2 f(x)dx=-4-1<=x<=0,f(x)x=-1,f(x)x=0f^(')(-0.5)=0f^(')(x)<0f^(')(2)=0f^(')(x)<02-\infty , and f^(')(2)=0, and f^(')(x)<0 for 2-\infty and \int_0^2 f(x)dx=-4.
(c) For -1<=x<=0,f(x) has a global min at x=-1,f(x) has a global max at x=0, and f^(')(-0.5)=0.
(d) f^(')(x)<0 for -\infty , and f^(')(2)=0, and f^(')(x)<0 for 2