Application of DerivativeHard
Question
If a, b > 0 and ᐃ (x) = 
, then -
, then -Options
A.ᐃ (x) is decreasing in (-
)
)B.ᐃ(x) is increasing in (
, ∞)
, ∞)C.ᐃ(x) has a local minimum at x =
D.ᐃ(x) is strictly increasing.
Solution
Given that ᐃ(x) = 
now,
ᐃ′(w)
or ᐃ′(x) = 3(x2 - ab)
sign scheme for ᐃ′(x)
∴ ᐃ(x) is increasing in (- ∞, -
) ∪ (
, ∞)
ᐃ(x) is decreasing in (-
).
ᐃ(x) has local minimum at x =
now,
ᐃ′(w)
or ᐃ′(x) = 3(x2 - ab)
sign scheme for ᐃ′(x)
∴ ᐃ(x) is increasing in (- ∞, -
) ∪ (, ∞)ᐃ(x) is decreasing in (-
).ᐃ(x) has local minimum at x =
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