Trig question

1. Jul 21, 2004

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).

2. Jul 22, 2004

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...

3. Jul 22, 2004

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:

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