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If f(x) is a differentiable function wherever it is continuous and f '(c1) = f '(c2) = 0, f ''(c1). f ''(c2) < 0, f(c1) = 5, f(c2) = 0 and (c1 < c2) Now answer the following questions,
Q. If f(x) is continuous in [c1, c2] and f ''(c1) - f ''(c2) > 0, then minimum number of roots of f '(x) = 0 in [c1 - 1, c2 + 1] is
1. 2
2. 3
3. 4
4. 5
32 roots??
clearly by f''(c2)-f''(c1) >0 f '(c1) = f '(c2) = 0, f ''(c1). f ''(c2) < 0 we find ..... at c2 we have minima and at c1 we have maxima
but f(c1)>f(c2)
so the graph will look like this in the extreme case [min roots] ....
[approx.]
clearly 2 roots .....
4U mean ans is 1st option 2
I got 1st option as ans
But ans is given as 4
I wanted to verify
3i think its 2 roots only some print error ....
unless c1-1 and c2+1 signifies sum thing ..........
