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If f(x) and g(x) are differentiable and increasing functions then which of the following functions alwasys increases? |
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Answer» Solution :GIVEN that f(x) and g(x) are increasing FUNCTIONS `therefore f(x) ge 0`and`g(x) ge 0` (i) iff(x)+g(x)=`f(x)+g(x)ge0` `therefore`f(x) + g(x) increases. (ii) f(x)g(x)=f(x)g(x)+f(x)g(x)the sign of which depends upon the sign of f(x) and g(x) also. So, f(x)g(x) MAY be increasing or decreasing. (iii) f(x)-g(x)=f(x)-g(x), may be positive or NEGATIVE so , f(x)-g(x) may be incresing or decreasing. (iv) `f(x)/g(x)=(f(x)g(x)-f(x)g(x))/g(x)^(2)`, may be positive or negative. So .`f(x)/g(x)`may be increasing or decreasing . |
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