Suppose fx 52 sin 26 pi x 26 i What is the maximum value o

Suppose f(x) = 5.2 sin (2.6 pi x + 2.6). i. What is the maximum value of f? ii. Suppose x greaterthanorequalto 0. What are the first two values of x (greater than or equal to 0) such that f(x) is maximum? iii. What is the minimum value of f? iv. Suppose x greaterthanorequalto 0. What are the first two values of x (greater than or equal to 0) such that f(x) is minimum?

Solution

Solution:

f(x) = 5.2sin(2.6x +2.6)

(i) as we know that maximum value of sin is 1

maximum of f(x)

f(x) = 5.2 x1

f(x) = 5.2

answer: (i) : 5.2

(ii) max of sin = 1

sin(2.6x +2.6) = 1

for first two values greater than 0 where f is maximum

x = ( 25 - 26 ) / 26 and (65 -26) /26

x= 0.643 and x = 2.185

(iii) minimum of sinx = -1

therefore minimum of f(x) = -5.2

(iv)

first two positive value where f is minimum

sin(2.6x +2.6) = -1

x = (15-26)/26 and x=(35-26)/26

x = 0.258 and x = 1.0278

Answer