Given the graph of y = cos theta on the interval 0 ≤ theta ≤ 2pi, for which value of theta does y have upward

Given the graph of y = cos theta on the interval 0 ≤ theta ≤ 2pi, for which value of theta does y have upward concavity?
a. Theta=0
b. Theta=1
c. Theta=2
d. None of these



Suppose p(x) is a twice-differentiable function such that p(1) = 3, p'(1) = 0, and p”(1) = -2. Which of the following is true?
a. There is a relative maximum at p(1)=3
b. There is a relative minimum at p(1)=3
c. There is a point of inflection at p(1)=3
d. None of these are true.

Given the graph of y = cos theta on the interval 0 ≤ theta ≤ 2pi, for which value of theta does y have upward concavity.
cos(0) = 1
cos(pi/2) = 0
cos(pi) = -1
cos(3pi/2) = 0
cos(2pi) = 1
So concave upward at cos(theta) = cos(pi) = -1
answer: d
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a. There is a relative maximum at p(1)=3
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The cosine curve has negative concavity between pi/2 and 3pi/2 and the value theta=2 is in that interval so the answer is c

2nd question answer is a because p' = 0 and p'' < 0