3.[-/6.66 Points]
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LARCALC12 3.1.001.
MY NOTES
ASK YOUR TEACHER
What does it mean to say that f(c) is the minimum of f on an interval I?
It means f(c) is the high
point of the graph of f on the interval I. That is, f(c) is less than or equal to f(x) for all x in I.
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4.[-/6.66 Points]
DETAILS
LARCALC12 3.4.015.EP.
MY NOTES
ASK YOUR TEACHER
Consider the following function.
y = 9x - 2 tan(x)
Find the first and second derivatives.
y'(x) = 9 - 2sec^2(x)
y''(x) = 4tan(x)sec^2(x)
Find any values of c such that y''(c) = 0. (Enter your answer as a comma-separated list. If any answer does not exist, enter DNE.)
Determine the open intervals on which the graph of the function is concave upward or concave downward. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
concave upward: (0, π/2) U (3π/2, 2π)
concave downward: (Ď€/2, 3Ď€/2)