InterviewSolution
Saved Bookmarks
| 1. |
Let f: Rto R be by f(x)=(x-1)(x-2)(x-5). Define F(x)=int_(0)^(x)f(t)dt,xgt0 Then which of the following options is/are correct ? |
|
Answer» `F(x) ne 0` for all `x in (0,5)` Since , `F(x)-int_(0)^(x) f(t)dt,x gt 0` So, `F'(x)=(x-2)(x-5)` Accroding to wavy curve method `(-""+""-""+)/(1"2"5)` F'(x) chages , it's sign form negative to positive at `x =1` and 5, So, F(x) has minima at ` x=1` and 5 and as F'(x) changes, it's sign from positive to negative at` x=2` so F(x) has maxima at ` x=2` ` because F(2)=int_(0)^(2) f(t)dt= int_(0)^(2)(t^2-8t^2+17t-10)dt` ` =[(t^4)/(4)-8(t^3)/(3)+17(t^2)/(2)-10T]_(0)^(2)` ` =4-(64)/(3)+34-20=38-(124)/(3)=-(10)/(3)` `because` At the point of maxima `x=2`, the functional value `F(2)=-(10)/(3)`, negative for the internal `x in (0,5)`, so `F(x)ne 0` for any value of `x in (0,5)`, Hence , OPTIONS (a),(b) and (d) are correct. |
|