MCV Test 2 Chapter 2 plus.... Wednesday March 4, 2009
1. [K3] Determine the derivative, from first principles for f(x) = .
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2. [K 3] Write the first line in determining given y = . DO NOT find the derivative, just show all of the steps by writing which function is being differentiated and which function it is with respect to.
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3. [K 3] Determine the absolute maximum value for f(x) = Justify your solution.
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4. [K 4] Differentiate f(x) = 3(2x - 1)4(2-3x)5. Express the answer in simplified factored form.
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5. [K 3] Given y = 4u - u2 and u = , determine when x = -3..
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6. [A 4] Determine the equation of the tangent to the curve y = at the point where x = -2.
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7. [A 3] During a fireworks display, a starburst rocket is shot upward with an initial velocity of 34.5 m/s from a platform 3.2 m high. The height, in metres, of the rocket after t seconds is represented by the function h(t) = -4.9 t2 +34.5t +3.2. Sometimes the rocket malfunctions and they do not explode. At what velocity would the unexploded rocket hit the ground?
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8. [A 4] The population of a certain type of berry bush in a conservation area is represented by the function p(t) = , where p is the number of berry bushes and t is the time, in years. What is the rate of change of the berry bush population at the time there are 40 berry bushes? Express answer correct to the nearest tenth. You may use a calculator to assist you in this question.
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9. [A 3]
A function g is defined by g(x) = 3x2 - x +1.The graph of y = f(x) and the tangent at x = 2 are shown on the right.
A new function is defined by
h(x) = 2f(x) - 4g(x) -3. Determine the slope of the tangent line to the graph of y = h(x) when x is 2. /