Max Value of f(x) for Positive x

[zero_eclipse]

For the function f(x) = 3sin bx + d where b and d are positive constants, determine an expression for the smallest positive value of x that produces the maximum value of f(x).

 

[zero_eclipse]

oops i guess i should post what i have:

well the smaller the period of the sin graph, the smaller the value of x

as for the largest maximum value would be the amplitude + d where as d increases, the larger the f(x)
3+d at 2pi/b

So how exactly do you put that as an expression? My teacher is quite picky about these little things...

 

[AKG]

You can see that this function has it's greatest value when sin(bx) has it's greatest value. sin(bx) has a maximum value of 1. You know that the smallest argument for the sine function that gives a value of 1 is $\pi /2$. Therefore:

$$bx = \pi /2$$

$$x = \frac{\pi}{2b}$$

I think you said something like $2\pi /b$ which is wrong. Anyways, the expression you're looking for is:

$$\frac{\pi}{2b}$$