What are the points of inflection of #f(x)=xcosx # on the interval #x in [0,2pi]#?

Answer 1

#f'(x)=cos(x)-xsin(x)#
#f"(x)=-2sin(x)-xcos(x)#
set #f"(x)=0# for points of inflection, x=0, 2.29

On your calculator let equation 1 be #y=2sin(x)# let equation 2 be #y=-xcos(x)# Find the points of intersection in #[0, 2pi]#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the points of inflection of ( f(x) = x \cos(x) ) on the interval ( x ) in ([0, 2\pi]), we need to find where the second derivative changes sign or equals zero. The second derivative is ( f''(x) = 2 \cos(x) - x \sin(x) ). We then solve ( f''(x) = 0 ) for ( x ) in the interval ([0, 2\pi]) and determine the intervals where the sign changes. Solving ( f''(x) = 0 ) yields solutions at ( x = \pi/2 ) and ( x = 3\pi/2 ). Then, we evaluate the sign of ( f''(x) ) in each interval between these points. The intervals where ( f''(x) ) changes sign indicate points of inflection. Therefore, there is one point of inflection at ( x = \pi/2 ) and another at ( x = 3\pi/2 ).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7