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If a continuous function f defined on th...

If a continuous function `f` defined on the real line R assume positive and negative values in R, then the equation `f(x)=0` has a root in R. For example, if it is known that a continuous function `f` on R is positive at some point and its minimum value is negative, then the equation `f(x)=0` has a root in R. Consider `f(x)= ke^(x)-x`, for all real x where k is a real constant.
The line `y=x` meets `y=ke^(x)` for `k le 0` at

A

no point

B

one point

C

two points

D

more than two points

Text Solution

Verified by Experts

The correct Answer is:
B
Let y=x intersect the curve `y=ke^(x)` at ecactly one opont when `k le0.`
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