For each of the following functions f(x) below : Find its limits limx→±[infinity]f(x) as x approachs ±[infinity] . Choose the values of x where f(x) is differentiable, i. e. f′(x) exists Choose the values of x where f(x) is also strictly increasing, i. e. f′(x)>0 . For f(x)=max(0,x) : (If the limit diverges to infty, enter inf for [infinity], and -inf for −[infinity] ) limx→−[infinity]f(x)=

See below

Step-by-step explanation:

then f(x)=0 if x<0 and f(x)=x if x≥0.

When x→-∞, f is the constant function zero, therefore . When x→∞, f(x)=x and x grows indefinitely. Thus

f is differentiable if x≠0. If x>0, f'(x)=1 (the derivative of f(x)=x) and if x<0, f'(0)=0 (the derivative of the constant zero). In x=0, the right-hand derivative is 1, but the left-hand derivative is 0, hence f'(0) does not exist,

f'(x)>0 for all x>0. Therefore f(x) is strictly increasing on the inverval (0,∞).