Question

What is the maximum value of f(x) = −3 sin(5x-4)? A. 5

B. 3
C. 4
D. 1.5
E. 15

Answer 1

The maximum value of f(x)=−3sin(5x−4) is 3.

The function f(x)=−3sin(5x−4) is a sinusoidal function, and its maximum value is the amplitude of the sine function, which is the absolute value of the coefficient of the sine term. In this case, the coefficient is -3, so the amplitude is 3.

Therefore, the maximum value of f(x) is 3. Among the given options, the correct one is: B. 3

Answer 2

The maximum value of the function f(x) = -3·sin(5·x - 4) is 3. The correct option is therefore;

B. 3

The steps to find the maximum value of the function are as follows;

The maximum value of the function, f(x) = -3·sin(5·x - 4), can be found from the extreme values of the sine function, which are +1, and -1

The maximum value of the function, f(x) = -3·sin(5·x - 4), is the point where the function representing the multiplicand of -3 is minimum or with a large -ve value

When sin(5·x - 4) = +1, we get;

-3·sin(5·x - 4) is; -3 × 1 = -3, which is the minimum point of the function

When sin(5·x - 4) = -1, we get;

-3·sin(5·x - 4) is; -3 × -1 = 3

The maximum value is 3

The largest -ve value of the function, sin(5·x - 4), which is -1, results in the maximum value of the function of 3