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"Let "F(x) =(f(x))^(2) +(f'(x))^(2),F(0)=7 where f(x) is thrice differentiable fucntion such that |f(x)|le1AAx in [-1,1]then prove the following . (i) there isatleast one point in each of the intervals (-1,-0) and (0,1) where |f'(x)|le2) (ii) there isatleast one point in eachof theintervals (-1,0) and (0,1) where F(x) le 5 (iii) there exits atleast one maxima ofF(x) " in "(-1,1) (iv) for somec in (-1,1) F(c )ge 7, F'(c )=0 " and "F''(c )le0 |
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