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IntroCal / Mr. Hansen |
Name: ________________________ |
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1/30/2007 |
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Quiz (50 points)
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1. |
For g(x) = cos(ln x), answer these questions. |
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(a) |
g¢(x) = ______________________________ |
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(b) |
Oops! This was my mistake. Explain why x = 0 is technically not a “critical value.” |
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(c) |
Explain why x = 1 is a “critical value.” |
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(d) |
Find the smallest critical value that is greater than 1. (Give exact value, no decimals.) |
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(e) |
State g(ep/4) in exact form (no decimals). |
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(f) |
Prove that (e2p, 1) is a local maximum. |
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2. |
For the function y = f (x) = x/(x2 + 1), answer these questions. |
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(a) |
Find an equation of the tangent line that passes through (1, ½). |
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(b) |
State Df, the domain of f. |
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(c) |
State Df ¢ , the domain of f ¢. |
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(d) |
Find all critical points of f without using your calculator. (Show work.) State the type (local min., local max., etc.) for each one. |
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3. |
Is it possible for a function f to have a critical point where f ¢(x) = 0, but where (x, f (x)) is neither a local minimum nor a local maximum? Explain. |