f(x)=3sin(/2) on the domanin [-2, 2] A) True or False, the function is an even f

ID: 2874015 • Letter: F

Question

f(x)=3sin(/2) on the domanin [-2, 2]

A) True or False, the function is an even function

B) True or False, the function is an odd function

C) Find the first derivative of f

D) Find all critical points of f

E) Identify those intervals where f is increasing and those intervals where f is decreasing

F) Use the first derivative test to identify local extrema

G) Find the second derivative of f

H) Identify those intervals where f is concave up and those intervals where f is concave down

I) Find all inflection points of f

J) Sketch the graph of f over the interval [-2, 2]

Answer:

Given that f(x)=3sin(/2)implies that f(x)=3(1)=3 since sin(/2)=1

therefore f(x)=3 which is a constant function

(A) since f(-x)=f(x)=3sin(/2). Hence f(x) is an even function

(B) Hence f(x) is not an odd function

(D) No critical points to the function f(x) as f(x) is constant function

(E)As f(x) is constant , f is neither increasing nor decreasing.

(F) No extrema

(G) The second derivative of f is zero as f(x) is constant

(H) no where f is concave up and f is concave down as f(x) is constant

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