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Let `f(x)` be a differentiable function on [0, 8]. Such that `f(1)=3,f(2)=1/2,f(3)=4,f(4)=-2,f(5)=6,f(6)=1/3,f(7)=-1/4` . Then the minimum number of points of intersection of the curves `y=f^(prime)(x)` and `y=f^(prime)(x)[f(x)]^2` is 10 (b) 6 (c) 11 (d) 25

Text Solution

Verified by Experts

The correct Answer is:
6
`f^(')(x)=f^(')(x)(f(x))^(2)`
Either `f^(')(x)=0` at least 4 roots
`f(x)=1` at least 5 roots
`f(x)=-1` at least 2 roots
at least 11 roots.
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