A1yeeMadanaban
A1yeeMadanaban A1yeeMadanaban
  • 23-09-2016
  • Mathematics
contestada

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?
f(x) = 5x^2 − 3x + 2, [0, 2]

Respuesta :

HomertheGenius
HomertheGenius HomertheGenius
  • 28-09-2016
The Mean Value Theorem:
If a function is continuous on [ a, b ] and differentiable on ( a , b ) than there is a point c in ( a, b ) such that:
f ` ( c )=  ( f ( b ) - f ( a ) ) / ( b - a )
f ` ( c ) = ( f ( 2 ) - f ( 0 ) ) / ( 2 - 0 )
f `( x ) = 10 x - 3
f ` ( c ) = 10 c - 3 
2 f ` ( c ) = 16 - 2
f ` ( c ) = 7
7 = 10 c - 3
c = 1
Answer:
          Yes, the function is continuous on [ 0, 2 ] and differentiable on ( 0, 2 ).
Answer Link

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