1995test1 - UNIVERSITY OF TORONTO SCARBOROUGH CAMPUS...

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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). [1] (i) This rational function has 3 zeros but its derivative has no zero. [1] (ii) This function has no zero, but its derivative has 3 zeros. [1] (iii) Neither this function nor its derivative take on a maximum value on the interval (- 1 , 1). [1] (iv) On [- 1 , 1], the derivative takes on its minimum inside the interval, but its maximum is taken on at an endpoint. [1] (v) There is no horizontal tangent. [1] (vi) There is a tangent that passes through the graph of the curve at the point of tangency (an inflection point). [1] (vii) The slope of any tangent line is positive. (A) (B) (i) (ii) (iii) (iv) (v) (vi) (vii) [4] (b) (i) State Rolles Theorem for rational functions. Clearly indicate what are the hypotheses and what is the conclusion....
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1995test1 - UNIVERSITY OF TORONTO SCARBOROUGH CAMPUS...

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