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Let f(x)={{:(|x^(3)+x^(2)+3x+sinx(3+sin(1)/(x)), x ne 0), (0,x=0):} Then the number of points where f(X) attians its minimum value is _______. |
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Answer» Let `g(x)=x^(3)+x^(2)+3x+sinx` `therefore g(x)=3x^(2)+2x+3+cosx` `=3(x^(2)+(2x)/(3)+1)+cosx` `=3{(x+1/3)^(2)+8/9}+coxgt0` and `2lt3+sin(1/x)lt4` Hence minimum value of `f(x) is 0 at x=0` Hence number of POINTS =1 |
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