Theory of Equations 5 Question 13

13. The function f(x) is

(a) increasing in t,14 and decreasing in 14,t

(b) decreasing in t,14 and increasing in 14,t

(c) increasing in (t,t)

(d) decreasing in (t,t)

Passage II

If a continuous function f defined on the real line R, assumes 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 values is negative, then the equation f(x)=0 has a root in R. Consider f(x)=kexx for all real x where k is real constant.

(2007, 4M)

Show Answer

Solution:

  1. As, f(x)=2(12x+3)

f(x)>0, when x>14 and

f(x)<0, when x<14.

It could be shown as



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