If f ( x ) is continuous in [ c 1 , c 2 ] and f ′′ ( c 1 ) − f ′′ ( c 2 ) 0 then the minimum number of roots of f ′ ( x ) = 0 in [ c 1 − 1 , c 2 + 1 ] is

Question

If f ( x ) is continuous in [ c 1 ​ , c 2 ​ ] and f ′′ ( c 1 ​ ) − f ′′ ( c 2 ​ ) > 0 then the minimum number of roots of f ′ ( x ) = 0 in [ c 1 ​ − 1 , c 2 ​ + 1 ] is

TestHub · Accepted Answer

Since f ′′ ( c 1 ) − f ′′ ( c 2 ) > 0 and f ′′ ( c 1 ) × f ′′ ( c 2 ) < 0 ⇒ f ′′ ( c 1 ) > 0 f ′′ ( c 2 ) < 0 It follows that f ′ ( x ) = 0 has at least four roots in the given interval

Mathematics - Application of Derivative Question with Solution | TestHub

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