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Let vec a=f(x) hat i-f'(x) hat j and ve...

Let `vec a=f(x) hat i-f'(x) hat j and vec b=g(x) hat i+g'(x) hat j` be two non-zero vectors and a twice derivable function `h (x)` be antiderivative of `f (x) g (x)`. If `vec a and vec b` are linearly dependent for exactly 4 differentvalues of `x in [0,4]` then find minimum number ofreal roots of `h'' (x) = 0` in `[0, 4]`.

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