Application of DerivativeHard
Question
If f(x) = xex(1-x), then f(x) is
Options
A.increasing in [-1/ 2,1]
B.decreasing in R
C.increasing inR
D.decreasing in [-1/ 2,1]
Solution
Given f(x) = xex(1-x)
⇒ f′(x) = ex(1-x) + xex(1-x) (1 - 2x)
= ex(1-x) [1 + x(1 - 2x)]
= ex(1-x) (1 + x - 2x2)
= - ex(1-x) (2x2 - x - 1)
= - ex(1-x) (x - 1)(2x + 1)
Which is positive in
Therefore, f(x) is increasing in
.
⇒ f′(x) = ex(1-x) + xex(1-x) (1 - 2x)
= ex(1-x) [1 + x(1 - 2x)]
= ex(1-x) (1 + x - 2x2)
= - ex(1-x) (2x2 - x - 1)
= - ex(1-x) (x - 1)(2x + 1)
Which is positive in
Therefore, f(x) is increasing in
.Create a free account to view solution
View Solution FreeMore Application of Derivative Questions
Number of tangents drawn from the point (-1/2, 0) to the curve y = e{x}. (Here { } denotes fractional part function)....The volume of metal in a hollow sphere is constant. If the inner radius is increasing at the rate of 1 cm/sec, then the ...The equation of the tangent to the curve y = cos x at x = π/3 is-...If f(x), for every nu8mber x, then the minimum value of f...The distance of normal from origin at any point θ to the curve x = a (cosθ + sinθ), y = a (sinθ W...