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PracticeMidtermIandII

# PracticeMidtermIandII - (5 Find where x 3-3 x 2-2 is...

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l Sample Midterm I and II (1) Calculate the derivatives. (a) d dx x 4 6 (b) d dx (tan x ) 2 (c) d dx y 3 e 2 y (d) d dx sin( x 2 + x ) (e) d dx e x x - a (f) h ( z ) = e sin z (2) Calculate the derivatives. (a) h ( z ) = e sin z (b) h ( s ) = log 5 (sin x ) (c) g ( t ) = t sin t (3) Let f(x)= x 3 - 3 x 2 - 2. (a) Find all critical numbers of f. (b) Find all inﬂection point of f. (c) Find all relative maximum and relative minimum using the ﬁrst deriv- ative test. (d) Find all relative maximum and relative minimum using the second derivative test. (e) Sketch the graph of y = f ( x ) (f) Find the absolute maximum of y=f(x) in [-1,4] (4) Find where x 3 - 3 x 2 - 2 is increasing. Explain your answer

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Unformatted text preview: (5) Find where x 3-3 x 2-2 is concave upward. Explain your answer. (6) Use the implicit diﬀerentiation to ﬁnd the equation of the tangent line to x 2 + y 2 = 4 at (1 ,-√ 3) (7) Let y = f ( x ) = x 3 + 2 x-2. Let g be the inverse function of f. Find the derivative of g at 10, g (10) (8) Judy is making a box from a 10 in × 20 in rectangle card board after cutting out 4 corners. Find how much square from the 4 corner should she cut out to have a maximum volume. 1 2 MAT125...
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PracticeMidtermIandII - (5 Find where x 3-3 x 2-2 is...

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