So f'(x)=2x+sinx.
F'(x) is odd function, so it is enough to discuss its comparison with 0 on (0, π/2).
On (0, π/2], f' (x) >: 0, so f(x) increases monotonically on (0, π/2].
On [-π/2,0] f' (x)
And f(0)=0- 1=- 1,? f(-π/2)=(-π/2)^2+ 1>; 0,f(π/2)=(π/2)^2- 1>; 0,
So the general graph is as shown in figure (1)? show
G(x)=|f(x)|- 1/2 zero. As long as the image of image |f(x)| has several intersections with the image of y= 1/2.
The image of |f(x)| just folds up the negative part of the original image of f(x). As shown in Figure (2), it can be seen that the number of zeros is four.
Summary of Youth League Branch Work 1
A year is fleeting. In a blink of an eye, our youth league branch has been busy fo