The function f is defined by f(x) = 3x - 4cos(2x + 1), and its derivative is f'(x) = 3 + 8sin(2x + 1). What are all values of that satisfy the conclusion of the Mean Value Theorem applied to f on the interval [-1, 2] ?

f ( x )  does not satisfy the mean value theorem

Step-by-step explanation:

The given data :-

Solution :-

i) f(x) is continuous on [ -1 , 2 ]

ii) f(x) is derivable on ( -1 , 2 )

f ( -1 ) = 3 * (-1 ) - 4 cos [ 2 * ( -1 )  + 1 ]  = - 3 + cos (-1 ) = - 3 - 4 * 0.9998 = - 6.992

f ( 2 ) = 3 * 2 - 4 cos ( 4 * 2 + 1 ) = 6 + 4 cos 9  = 6 - 3.9507 = - 3.04924

iii) f ( -1 ) ≠ f ( 2 )

f ( x ) is not real valued function so it does not satisfy the mean value theorem

hi,

you half the rectangle that you ae asking about so then you would see the scale factor of 1/2 the one u have selected, the one on top is half.

hope this !