Re: DSE 2010: Q. 58 & 59

Posted by Sinistral on Jun 09, 2013; 8:20pm
URL: http://discussion-forum.276.s1.nabble.com/DSE-2010-Q-58-59-tp7582078p7582079.html

58)
a < b
f(a)=0 and f(b)=0 => there has to be atleast one minima/maxima in between (a,b). (ignoring the case wherein f(x)= 0 for all x belonging to [a,b])

f"(x)+f'(x) -1 =0
f'(x) has to be zero in between (a,b) because of the above inference.
So f"(x)-1=0 => f"(x) =1 => f"(x) >0 => f(x) has a minima in between (a,b)
it cant have a maxima since f"(x) is always greater than zero in between (a,b)
so option (b)

59)
once (58) is clear 59 is obvious.
if the graph of f(x) goes above x axis in between (a,b) then it has to come down to x axis at x=b (since f(b)=0 ). it wud lead to a local maxima in between (a,b). but we just saw that f(x) doesnt have a maxima in between (a,b). that means f(x) will never go above x axis in between (a,b). so option a