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Unformatted text preview: UNIVERSITY OF TORONTO SCARBOROUGH CAMPUS MATA26Y October 30, 1995 TERM TEST I 1. (a) Match the following statements with one (or both) of the pictures below, by checking the appropriate column(s).  (i) This rational function has 3 zeros but its derivative has no zero.  (ii) This function has no zero, but its derivative has 3 zeros.  (iii) Neither this function nor its derivative take on a maximum value on the interval (- 1 , 1).  (iv) On [- 1 , 1], the derivative takes on its minimum inside the interval, but its maximum is taken on at an endpoint.  (v) There is no horizontal tangent.  (vi) There is a tangent that passes through the graph of the curve at the point of tangency (an inflection point).  (vii) The slope of any tangent line is positive. (A) (B) (i) (ii) (iii) (iv) (v) (vi) (vii)  (b) (i) State Rolles Theorem for rational functions. Clearly indicate what are the hypotheses and what is the conclusion....
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