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Let h(x) =f(x)-a(f(x))^(3) for every real number x h(x) increase as f(x) increses for all real values of x if |
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Answer» `a in (0,3)` or `h(X)=f(x)-2af(x)f(x)+3a(f(x))^(2)f(x)` `=f(x)[3a(f(x))^(2)-2af(x)+1]` Now h(x) increase if f(x) increase and `3a(f(x))^(2)-2af(x)+1gt0for all x in R` or `3agt0 and 4A^(2)-12ale0` or `AGT0 and a in [0,3]` or `a in [0,3]` |
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