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The interval in which y = x2e- x is increasing is
(A) (- ∞, ∞) (B) (- 2, 0) (C) (2, ∞) (D) (0, 2)
Solution:
Increasing functions are those functions that increase monotonically within a particular domain,
and decreasing functions are those which decrease monotonically within a particular domain.
We have,
y = x2e- x
Therefore,
dy/dx = 2xe- x - x2e- x
= xe- x (2 - x)
Now,
dy/dx = 0
Hence, x = 0 and x = 2
The points x = 0 and x = 2 divide the real line into three disjoint intervals
i.e., (- ∞, 0) , (0, 2) and (2, ∞)
In intervals (- ∞, 0) and (2, ∞), f' (x) < 0 as e- x is always positive.
Hence, f is decreasing on (- ∞, 0) and (2, ∞)
In interval (0, 2) ,
f' (x) > 0
Hence, f is strictly increasing in (0, 2)
Thus, the correct option is D
NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.2 Question 19
The interval in which y = x2e- x is increasing is (A) (- ∞, ∞) (B) (- 2, 0) (C) (2, ∞) (D) (0, 2)
Summary:
For the function y = x2e- x, f is strictly increasing in (0, 2) Thus, the correct option is D. The points x = 0 and x = 2 divide the real line into three disjoint intervals
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