Show that the function f(x) = x2 isa. strictly increasing on [0, ∞]

1.	Show that the function f(x) = x2 isa. strictly increasing on [0, ∞]b. strictly decreasing on [0, ∞]c. neither strictly increasing nor strictly decreasing on R
Answer» Domain of function is R. f’(x) = 2x for x>0 f’(x)>0 i.e. increasing for x<0 f’(x)<0 i.e. decreasing hence it is neither increasing nor decreasing in R

Show that the function f(x) = x2 isa. strictly increasing on [0, ∞]b. strictly decreasing on [0, ∞]c. neither strictly increasing nor strictly decreasing on R

Answer»

Domain of function is R.

f’(x) = 2x

for x>0 f’(x)>0 i.e. increasing

for x<0 f’(x)<0 i.e. decreasing

hence it is neither increasing nor decreasing in R