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Math16Apexam2

# Math16Apexam2 - bridge at a height of 32 feet above the...

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Math 16A: Practice problems for Midterm 2 Note: The midterm itself will not be this long. These are just some problems to get you ready. Problem 1. Find the derivatives of the following func- tions. (a) f ( x ) = ( x 2 + 1)( x - 5) (b) g ( x ) = x 2 +1 x - 5 (c) h ( x ) = sin( x 2 - x + 1) (d) k ( x ) = (cos( x ) + x ) 3 (e) r ( x ) = ( x 3 + x 2 ) 5 (f) s ( x ) = x 2 + x + 1 (g) t ( x ) = sin( x ) cos( x ) (h) u ( x ) = tan( x ) (i) v ( x ) = q x + x 2 (j) w ( x ) = sin( x ) · ( x 3 - cos( x )) 2. Using the deﬁnition of the derivative, ﬁnd the deriva- tive of f ( x ) = 3 x . 3. Find the equation of the line that is tangent to the graph of f ( x ) = x 3 + x - 1 at the point (0 , - 1) . 1

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4. A spherical balloon is being inﬂated at a rate of 6 cubic inches per second. How quickly is the radius, r , growing when r = 3 inches? 5. A rock, thrown upward at 16 feet per second from a
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Unformatted text preview: bridge at a height of 32 feet above the water below, has a height (in feet) given by h ( t ) =-16 t 2 + 16 t + 32, where t is measured in seconds. (a) How long does it take the rock to hit the water? (b) What is the velocity of the rock as a function of time? (c) What is the velocity of the rock when it hits the water? (d) What is the average velocity of the rock while it is in the air? 6. Using the deﬁnition of the derivative, ﬁnd the deriva-tive of f ( x ) = x 2 . 7. What is the best linear approximation of the func-tion f ( x ) = √ x 2 + 1 near the point (0 , 1) ? 2...
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Math16Apexam2 - bridge at a height of 32 feet above the...

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