Unformatted text preview: (6%) (c) Find the critical points, and ﬁnd where f is increasing and decreasing. Determine whether the critical points are local maxima, local minima, cusps, vertical tangents, or none of the above. (5%) (d) Find where f is concave up and concave down and locate the points of inﬂection. (5%) (e) Sketch the graph of f ( x ) , using the information found above. 4. (5%) (a) State the formal deﬁnition of lim x → a + f ( x ) = ∞ . (5%) (b) Prove, using the deﬁnition above, that lim x → 1 + 1 x1 = ∞ . 5. (5%) (a) State the Mean Value Theorem. (9%) (b) By applying the Mean Value Theorem to f ( x ) = √ x , show that 1 11 < √ 10210 < 1 10 . (10%) 6. Show that no two points on the curve y = x 4 + 2 x 2x share a common tangent line. 1...
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 Spring '08
 UPPAL
 Calculus, Derivative, Mean Value Theorem, Mathematical analysis, Convex function

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