TUDIUL COLICUL UITS. 1. [2] Consider the graph of g(x) shown below. STU 24/ 6 8
ID: 2891706 • Letter: T
Question
TUDIUL COLICUL UITS. 1. [2] Consider the graph of g(x) shown below. STU 24/ 6 8 10 y= g(x) (a) If g(x) is the first derivative of f(x), what is the nature of f(x) when x = 27 OA. f(x) has a local maximum at x=2. OB. f(x) is decreasing at x=2. Oc. f(x) has a local minimum at x=2. OD. f(x) is increasing at x= 2. (b) If g(x) is the second derivative of f(x), what is the nature of (x) when x = 27 O A. f(x) is concave down at x=2. OB. f(x) is concave up at x=2. Oc. f(x) has an inflection point at x=2.Explanation / Answer
1.
g(x)=f'(x)
when f'(x) is negative then f(x) is decreasing
f'(x) is positive then f(x) is increasing
f'(x)=0 then function has maximum or minimum at x
a.
g(x)=f'(x)
from the graph we can infer that g'(2) is negative
so,f(x) is decreasing at x=2
answer: B
b.
g(x)=f"(x)
f"(2)<0
so f(x) is concave downward at x=2
Answer:
Option A
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