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Consider the function h(x)=(g^(2)(x))/(2)+3x^(3)-5, where g(x) is a continuous and differentiable function. It is given that h(x) is a monotonically increasing function and g(0) = 4. Then which of the following is not true ? |
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Answer» `g^(2)(1)gt10` `h'(x)gt0` `rArr""g(x)g'(x)gt-9x^(2)` `rArr""int_(0)^(1)g(x)g'(x)dxgt-int_(0)^(1)9x^(2)dx` `rArr""((g(1))^(2)-(g(x))^(2))/(2)gt-3(1-0)` `rArr""(g(1))^(2)-16gt-6` `rArr""(g(1))^(2)gt10` `""int_(-1)^(0)g(x)g'(x)dx gt -int_(-1)^(0)9x^(2)dx` `rArr""((g(0))^(2)-(g(-1))^(2))/(2)gt-3(0-(-1))` `rArr""16-(g(-1))^(2)gt-6` `rArr""(g(-1))^(2)lt22` `""h(5)gth(0)` `rArr""h(5)gt(g^(2)(0))/(2)+3(0)-5=3` |
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