Which shows a difference of squares?
1 answer:
A difference of squares must be a binomial, so we want two terms. This rules out the third and fourth options.
If we look at the first two, we must check that both terms are perfect squares.
Look at the first one: is a perfect square (it's
), but
is not a perfect square, because 10 is not a perfect square.
On the other hand, if we look at the second option, is the square of
, and
is clearly the square of
. So, this is the difference of two squares.
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Answer:
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,∞).