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 function is monotonically decreasing at the point...If sum of n terms of a sequence is given by Sn = 3n2 - 5n + 7 & tr represents its rth term, then -...The slope of the tangent to the curve xy + ax - by = 0 at the point (1, 1) is 2, then values of a and b are respectively...The angle of intersection between the curvesy2 = 8x and x2 = 4y - 12 at (2, 4) is-...Let f and g be increasing and decresing functions respectively from [0, ∞) to [0, ∞) Let h(x) = f (g(x)). If...