If f(x) is twice differentiable function such that f(a)=0, f(b)=2, f(c)=1, f(d)=2 , f(e)=0 , where a

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If f(x) is twice differentiable function such that f(a)=0, f(b)=2, f(c)=1, f(d)=2 , f(e)=0 , where a < b < c < d < e , then the minimum number of zeros of g(x)= f^ (x) ^2+f^ (x) f(x) in the interval [a, e] is

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Correct answer: 6

Let, g(x)= d d x [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 aligned & g(x)=0 & h(x)=0 & f(x)=0 or f^ (x)=0 & If f(x)=0 has 4 minimum solutions, & f^ (x)=0 has 3 minimum solutions, & h(x)=0 has 7 minimum solutions, then & h^ (x)=g(x)=0 has 6 minimum solutions. & aligned

If f(x) is twice differentiable function such that f(a)=0, f(b)=2, f(c)=1, f(d)=2 , f(e)=0 , where a < b < c < d < e , then the minimum number of zeros of g(x)= f^ (x) ^2+f^ (x) f(x) in the interval [a, e] is

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