The derivative of the function g is g\'(x) = cos(sin x). At the point where x =
ID: 2837952 • Letter: T
Question
The derivative of the function g is g'(x) = cos(sin x). At the point where x = 0 the graph of g 1. is increasing II. Is concave down III. Attains a relative maximum point (A) I only (B) II only (C) III only (D) I and III only (E) I. II. III 2. The graph of the derivative of a function f is shown to the right. Which of the following is true about the function f? I. f is increasing on the interval (-2, 1). II. f is continuous at x = 0. III. F has an inflection point at x = -2. (A) I only (B) II only (C) III only (D) II and III inly (E) I, II, III 3. If functions f and g are defined so that f'(x) = g'(x) for all real numbers x with f(1) = 2 and g(1) = 3, then the graph of f and the graph of g (A) intersect exactly once; (B) intersect no more than once; C. do not intersect D. could intersect more than once; E. have a common tangent at each point6 of tangency.Explanation / Answer
1)g'(0)=cos(0)=1
Therefore g is increasing.
g''(x)=-Sin(sin x)*Cos(x)
g''(0)=0
Therefore, not concave down.
Also, no relative maxima since g'(0) is not zero. Only I is correct. Therefore, a) is correct.
b)f is increasing on (-1,2). Therfore I is false.
II is correct.
Inflection point is at x=-1, 3
Therefore only II is correct. B) is correct.
3)Do not intersect since g will always be above f.