Please answer the following Let f (r) sin on the interval [0,2m). Fill in the bl

Question

Please answer the following

Let f (r) sin on the interval [0,2m). Fill in the blanks below 1. f is increasing for r E 2. f is decreasing for r E 3. The local maxima of f occur at r 4. The local minima of f occur at r 5. The absolute maximum of f occurs at r 6. The absolute minimum of f occurs at r 7. f s concave up for a E 8. f is concave down for r E e point(s) of inflection of f occu y f(r) has vertical asymptotes at r 10. The curve 11. The curve y T has a y-intercept is on the y-axis) at y TT

Explanation / Answer

f(x) = x + sinx

f'(x) = 1+cosx

1 + cosx is always greater than or equal to 0

1.so f(x) is always increasing.

2/so f(x) increasing for [0,2pi]

f(x) decreasing for none.

f'(x) =0

=> cosx = -1

=> x=pi.

at x=pi

f(x) = pi + sin(pi) = pi.

3.so local minima occurs at x=pi value of f(x) =pi.

4.there is no local maxima.

5.absolute maximum of f(x) occurs at x =2pi.

it's value = 2pi + sin(2pi) = 2pi

6.absolue minima occurs at x =0

f(x) = 0 + sin(0) = 0.

7.concave up for [0,2pi]

8. concvae down for none

9.points of infelction occur at x = pi.

10.no vertical assymptote.

11. y intercept at y=0

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---