Find the points at which the tangent line is horizontal for the given interval. F(x)=cosx-sinx [0,2pi]

Step-by-step explanation:

For the tangent line to be horizontal, the derivative of the function at that point must be 0.

Thus, let’s first take the derivative of our function:

Differentiate:

Now, let’s set our derivative equal to 0:

Let’s multiply everything by a negative:

To solve for x, we can subtract sin(x) from both sides. This gives us:

Now, we can refer to the unit circle. First, remember that the only points for which cosine is equal to sine is at the π/4 points. That is, π/4, 3π/4, 5π/4 or 7π/4.

However, cosine is equal to negative sine. The only two quadrants for which cosine and sine are the same but also have opposite signs is QII and QIV.

Therefore, our answers are 3π/4 and 7π/4.

$2416.6

step-by-step explanation:

per hour = $ 25

total work time = 35

commission = 15%

total she has to make = $ 4,500

let she sold x dollar products

so her commission will be 15 % of x

now

total = weekly basic pay + commission

4500= (25*35) + 15 % of x

4500=875 + * x

4500-875 =   * x

3625= * x

multiplying wwith 100 on both sides gives

36250 = 15 x

now

x =  

x= $2416.6