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For a twice differentiable function f(x)...

For a twice differentiable function `f(x),g(x)` is defined as `g(x)=f^(prime)(x)^2+f^(prime)(x)f(x)on[a , e]dot` If for `a

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The correct Answer is:
6
Let `g(x) = (d)/(dx) [ f(x) * f' (x)]`
To get the zero of ` g(x)`, we take function
` " " h (x) = f (x) * f' (x)`
between any two roots of `h(x) `, there lies atleast one root of `h' (x) = 0`.
`rArr g (x) = 0 rArr h(x) = 0`
`rArr f(x) = 0 or f ' (x)=0`
If `f (x) = 0 ` has 4 minimum solutioins.
`f ' (x) = 0 ` has 3 minimum solutions.
`h (x) = 0 ` has 7 minimum solutions.
`rArr h ' (x) = g(x) =0` has 6 minimum solutions.
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