Question

f''(x) = sin (2x) - cos (4x)
Number of points of inflection of f(x) in [0, 10]?

Answer 1

This is actually a very good question.

Inflection points occur when the second derivative is equal to zero. You already have the second derivative and so you will just equate the formula you have to zero.
So it would be sin(2x) - cos(4x) = 0
sin(2x) = cos(4x)
now use trigonometric identities to simplify the following equation. Try to get all of the variables into one trigonometric identity. Like all of them to be sin, cos etc..

Hope this helps.

Answer 2

to simplify use the identity
cos 4x = 1 - 2 sin"2 (2x)

Answer 3

yeah but sin(2x) = 2sinxcosx, you also need to get rid of the sin though.

Answer 4

no form an equation in sin2x and sol ve for it
then you can find 2x then x

Answer 5

I evaluated it, you have to use quadratic formula finally after you have 2(sin(2x)^2 + sin(2x) - 1. But the thing is, I have found out there are 10 points of inflection, but the book from which I've taken this from has mentioned 7 as the answer..

Answer 6

hmmm sorry i have to go now