Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

(a) Find the intervals on which $f$ is increasing or decreasing.(b) Find the local maximum and minimum values of $f .$(c) Find the intervals of concavity and the inflection points.$f(x)=\sin x+\cos x, \quad 0 \leqslant x \leqslant 2 \pi$

A. increasing: $\left(0, \frac{\pi}{4}\right),\left(\frac{5 \pi}{4}, 2 \pi\right) \quad$ decreasing: $\left(\frac{\pi}{4}, \frac{5 \pi}{4}\right)$B. local maximum: $\left(\frac{\pi}{4}, \sqrt{2}\right) \quad$ local minimum: $\left(\frac{5 \pi}{4},-\sqrt{2}\right)$C. $\left(\frac{3 \pi}{4}, f\left(\frac{3 \pi}{4}\right)\right)=\left(\frac{3 \pi}{4}, 0\right)$$\left(\frac{7 \pi}{4}, f\left(\frac{7 \pi}{4}\right)\right)=\left(\frac{7 \pi}{4}, 0\right)$

Calculus 1 / AB

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 3

Derivatives and the Shapes of Graphs

Derivatives

Differentiation

Applications of the Derivative

Oregon State University

Harvey Mudd College

Idaho State University

Lectures

04:40

In mathematics, a derivati…

44:57

In mathematics, a differen…

06:26

(a) Find the intervals on …

05:55

08:06

03:26

04:07

02:09

06:24

02:51

01:49

05:54

04:12

07:44

03:30

(a) Find the intervals of …

03:12

03:23

05:45

a. Find the local extrema …

05:23

for this question. We first right out the first of the narrative and the second purity of it, um, self apart. A. We want to find an increasing and decreasing the role. So just said eff Primakov zero's air to solutions. Be careful. In this case, the Tomei's from 0 to 2 pi. So if time cause zero has two solutions in the art A too high, which are, however, floor in the high. Ah, five powerful. So we have these two solutions for this. If primary cause zero on them units we need you can see the three sub intervals. So 1st 1 is from zero to a pyre for so over this in Perot, the first of the narrative is positive. Um, therefore f seem crazy. And the for the second of room pi over 4 to 5 higher, full if prime is negative. So it's decreasing and the from five higher 4 to 2 pi. Um, the first of the curative is positive. So it seem crazy again. Now for here we can cruel. That's for part B. Um, at X equals two pi powerful. There is a low Comex. So with value F. Kyra full, you caused to write off to and for the second of the 13 travel when X equals 25 high or four, it's actually your loco minimum with Manlio F five pyre for because to minors of to. So this is for Poppy. As for posse, we need to use the second narrative and just said the second curative because zero. So again we have two solutions. X equals two, three high or four and X equals 27 pyro awful, and we also need to consider three intervals. So from zero 23 high or full, the second that they're cave is negative. So it's concave downward from three PIRA 4 to 7 pilot. Awful. The second figurative is positive. So it ikan caves upward in the front. Seven pira for to the right and the point to a pie. The sec on the beer it if it's negative again. So it's ah, downward. Um, with this result, we can crew leads if has to inflection points. We tried X equals 23 pyre for and the X equal to seven pyre for

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, a derivative is a measure of how a function changes as its i…

In mathematics, a differentiation rule is a rule for computing the derivativ…

(a) Find the intervals on which $f$ is increasing or decreasing.(b) Find…

(a) Find the intervals on which $ f $ is increasing or decreasing.(b) Fi…

(a) Find the intervals of increase or decrease.(b) Find the local maximu…

a. Find the local extrema of each function on the given interval,and say…

00:34

Find the exact value of each expression (without acalculator.)$$…

01:46

If $f(x)=e^{x}-2,0 \leqslant x \leqslant 2,$ find the Riemann sum with$n…

00:48

Simplify the expression.$\tan \left(\sin ^{-1} x\right)$

02:08

$1-38=$ Find the limit. Use l'Hospital's Rule where appropriate.

04:11

00:32

Use the properties of logarithms to expand thequantity.$$\log _{…

11:18

Consider the following problem: A farmer with 750 $\mathrm{ft}$ offencin…

00:26

(a) What is the natural logarithm?(b) What is the common logarithm?(…

01:25

Verify that the function satisfies the hypotheses of the Mean Value Theorem …

01:38

Find the most general antiderivative of the function(Check your answer b…