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Let f(x) = - (x)/(sqrt(a^(2) + x^(2)))- ...

Let `f(x) = - (x)/(sqrt(a^(2) + x^(2)))- (d-x)/(sqrt(b^(2) + (d-x)^(2))), x in R`, where a, b and d are non-zero real constants. Then,

A

is not a continuous function of x

B

f is neither increasing nor decreasing function

C

f is an increasing function of x

D

f is a decreasing function of x

Text Solution

Verified by Experts

The correct Answer is:
C
`f (x) = (x)/( sqrt(a ^(2) + x ^(2)))- ((d -x ))/( sqrt(b ^(2) + (d-x )^(2)))`
`f'(x) (sqrt(a ^(2) + x ^(2)). 1 -x 1/2. (2x )/(sqrt(a ^(2) + x ^(2 ))))/((a ^(2) + x ^(2)))- ([sqrt(b ^(2) + (d-x)^(2)) (-1)+ (d-x). (1)/(2) [2 (d -x) (1))/(sqrt(b ^(2) + (d-x)^(2)))])/((b ^(2) + (d-x )^(2)))`
Upon simplifying
`f '(x) = (a^(2))/((a ^(2) + x ^(2)))+ (b^(2))/((b ^(2) + (d -x )^(3)) 6(3//3))" "therefore f` is increasing
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