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UFCalcSet23

# UFCalcSet23 - Exercises UF Calculus Set 23 1 Examine the...

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Exercises UF Calculus Set 23 1. Examine the graph shown. Estimate the value c guaranteed by the Mean Value Theorem, and also f 0 ( c ) , on the intervals: [ - 6 , 0 ] ; [ - 5 , 6 ] ; [ 5 , 8 ] 2. Determine whether Rolle’s Theorem can be applied to the function on the given interval; if so, ﬁnd the value(s) of c guaranteed by the theorem. (a) f ( x ) = x ( x + 2) on [ - 2 , 0 ] (b) f ( x ) = x (2 - x ) on [ 0 , 2 ] (c) f ( x ) = x 2 / 3 + x on [ - 1 , 0 ] (d) f ( x ) = x 1 / 3 - x on [ - 1 , 1 ] (e) f ( x ) = ln(1 - sin( x )) on [ 0 , 2 π ] (f) f ( x ) = ln(2 - sin( x )) on [ 0 , 2 π ] (g) f ( x ) = 1 + | 2 x - 1 | on [ 0 , 1 ] (h) f ( x ) = x 4 ( x - 1) 3 on [ 0 , 1 ] 3. Determine whether Mean Value Theorem can be applied to the function on the given interval; if so, ﬁnd the value(s) of c guaranteed by the theorem. (a) f ( x ) = x 3 on [ 0 , 3 ] (b) f ( x ) = x + x 3 on [ - 1 , 1 ] (c) f ( x ) = x + 1 x on [ - 1 , 1 ] (d) f ( x ) = x + 1 x on [ 1 , 4 ] (e) f ( x ) = x - 1 x + 1 on [ 0 , 2 ]

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UFCalcSet23 - Exercises UF Calculus Set 23 1 Examine the...

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