Max Value of f(x) for Positive x

AI Thread Summary
The function f(x) = 3sin(bx) + d reaches its maximum value when sin(bx) equals 1, which occurs at bx = π/2. Therefore, the smallest positive value of x that produces this maximum is x = π/(2b). The maximum value of f(x) is determined by the amplitude plus the constant d, resulting in a maximum of 3 + d. As the value of d increases, the overall maximum of f(x) also increases. The correct expression for the smallest positive x that maximizes f(x) is π/(2b).
zero_eclipse
Messages
2
Reaction score
0
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).
:confused:
 
Mathematics news on Phys.org
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...
 
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}
 
Thread 'Video on imaginary numbers and some queries'
Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Thread 'Unit Circle Double Angle Derivations'
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
Back
Top