Math 16a quiz 3 find all relative minima and maxima of the

Question

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).