A) An increasing function
B) A decreasing function
C) A constant function
D) Data insufficient
Correct Answer: A
Solution :
\[\frac{d}{dx}(g'(x){{e}^{-\,3x}})>3.\,{{e}^{-\,3x}}\] |
\[\frac{d}{dx}(g'(x){{e}^{-\,3x}}+{{e}^{-\,3x}})>0\] |
\[\Rightarrow {{e}^{-3x}}(1+g'(x))\] is an increasing function. |
Now, \[{{e}^{-3x}}(1+g'(x))>(g'(0)+1)\] |
\[\Rightarrow x>0\] |
\[\Rightarrow g'(x)+1>0\] |
\[\Rightarrow g(x)+x\]is an increasing function. |
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