Use process of optimization

Do you mean f(x) = e^{-x} sin(2x)?

f'(x) = e^{-x} (2cos(2x) - sin(2x))

Solve f'(x) = 0 for extreme values,

tan(2x) = 1/2

x = .2318 rad , f(.2318) = .3547 <==Answer

Use process of optimization

Tutors, sign in to answer this question.

Do you mean f(x) = e^{-x} sin(2x)?

f'(x) = e^{-x} (2cos(2x) - sin(2x))

Solve f'(x) = 0 for extreme values,

tan(2x) = 1/2

x = .2318 rad , f(.2318) = .3547 <==Answer

Grigori S. | Certified Physics and Math Teacher G.S.Certified Physics and Math Teacher G.S.

The way they write equations and formulas sometimes is incorrect. You can write the same function in the way as Robert J. did, or as f(x) = exp(-xsin2x). If the exp(-x) is to be multiplied by sin(2x) then it is to be included in parenthesis, such as f(x) = exp(-x) sin(2x) , which is a totally different function. If we take

f(x) = exp( -xsin(2x)) then f'(x) = 0 if tan(2x) =-2x. This equation can be satisfied if x = 0 which is visible

without differentiation. If f(x) = exp(-x) sin (2x) then f'(x) = exp(-x)(2cos(2x) -sin(2x)) = 0 or

tan(2x) = 2 x = (1/2) atan(2) (cos(2x) = 1 and can be a divisor)

Because tan (2x) is a periodic function with the period = pi, we can write more common solution in the following way: x = (1/2)(atan(2x) +(or -) pin)

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

## Comments

it is e minus x

Thank you so much, Robert! Can you, please, also show how did you find x.