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Suppose f is a differentiable function on the interval [ 0 , 2 ] [0,2 ]and the derivative does not vanish at any point in that interval. Then f f can only have extrema at x = 0 x=0 or x=2. True or False ? With reason x = 2

Suppose f is a differentiable function on the interval [0,2] [0,2 ]and the derivative does not vanish at any point in that interval.
Then ff can only have extrema at x=0x=0 or x=2. True or False ? With reasonx=2

Grade:Upto college level

1 Answers

PASUPULETI GURU MAHESH
126 Points
6 years ago
TRUE, SINCE THE FUNCTIONderivative does not vanish at any point in that interval. SO THERE IS NO POSSIBLE TO DETERMINE CRITICAL POINTS.AND THERE IS NO CRITICAL POINTS OF THE FUNCTION WE FIND LOCAL EXTREME VALUES BY USING END POINTS. SO F HAVE extrema at x=0x=0 or x=2. IS True LOCAL

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