theorem 1.1

Select the statement that explains why the mean value theorem does not apply to the function f ( x ) = | x | in the interval [-1, 1]. => | x | is not continuous in (-1, 1) or | x | is not differentiable in (-1, 1) or | x | is not..

Select the statement that explains why the mean value theorem does not apply to the function f ( x ) = e 1 x in the interval [-1, 1]. => f ( x ) is continuous in [-1, 1]. or f ( x ) is not continuous in [-1, 1]. or f ( ..

Use Rolle's Theorem to determine the value of c such that f ′ ( c ) = 0, if f ( x ) = x 2 - 1 in the interval [- 1, 1]. => - 2 or 0 or 2 or - 1 or 1..

Use Intermediate Value Theorem to choose the correct statements from the following for the function f ( x ) = 2 x x 2 + 4 . I. f ( x ) has a zero on [- 1, 1] II. f ( x ) has no zero on [- 2, - 1] III. f ( x ) has a zero on [1, 2] IV. f ( x ) has a z..

x + 1 = 1 (Theorem 2a) In particular for x = 0, we have 0 + 1 = 1 (1) x.0 = 0 (Theorem 2b) In particular, for x =1 1.0 = 0 0.1 = 0 (3a) (2) From (1) and (2), we have For 0 B, 0 + ..

Question: Find the image of the point (-1,1) w.r.t to the line 3x + 4y = 32. Answer: Let the image of the point P (-1,1) about the line AB be Q (h,k). PQ is perpendicular to AB and is bisected at C. ..

The proof follows from theorem 2, P( f ) C = 1 - P( f ) = 1 - 1 = ..