Reference no: EM131075346
MATH 16A QUIZ 3-
(1) Let f(x) = x3 - 3x defined on R whose graph is as follows:
(a) T / F: "The function f(x) has two relative minima."
(b) T / F: "The function f(x) has one absolute maximum."
(c) T / F: "The function f(x) has three inflection points."
(d) T / F: "The point (0, f(0)) is an inflection point."
(e) T / F: "The point (1, f(1)) is an inflection point."
(f) T / F: "The point (-1, f(-1)) is an inflection point."
(g) T / F: "At (2, f(2)), the function f(x) is concave up and increasing."
(h) T / F: "At (-2, f(-2)), the function f(x) is concave down and decreasing."
(2) Suppose that f is a function defined on all of R such that its derivative f' is x3 - 3x.
(a) T / F: "The function f(x) has one relative minimum."
(b) T / F: "The function f(x) has three horizontal tangent lines."
(c) T / F: "The point (√3, f(√3)) is a relative maximum."
(d) T / F: "The point (0, f(0)) is an inflection point."
(e) T / F: "The point (1, f(1)) is an inflection point."
(f) T / F: "The point (-1, f(-1)) is an inflection point."
(g) T / F: "At (2, f(2)), the function f(x) is concave up and increasing."
(h) T / F: "At (-2, f(-2)), the function f(x) is concave down and decreasing.
(3) Find all relative minima and maxima of the function f(x) = x3 -12x-1 (and indicate whether each point is a minimum or maximum).
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