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 =
Create a free account to view solution
View Solution FreeMore Application of Derivative Questions
The equation of normal to the curve y = x3 − 2x2 + 4 at the point x = 2 is-...If f(x), for every nu8mber x, then the minimum value of f...The slopes of the tangents to the curve y = (x + 1) (x − 3) at the points where it crosses x- axis are -...The curve y = has...The slope of the curve y = sin x + cos2 x is zero at the point, where-...