The value of the derivative at the maximum or minimum for a continuous function must be zero.
<h3>What happens with the derivative at the maximum of minimum?</h3>
So, remember that the derivative at a given value gives the slope of a tangent line to the curve at that point.
Now, also remember that maximums or minimums are points where the behavior of the curve changes (it stops going up and starts going down or things like that).
If you draw the tangent line to these points, you will see that you end with horizontal lines. And the slope of a horizontal line is zero.
So we conclude that the value of the derivative at the maximum or minimum for a continuous function must be zero.
If you want to learn more about maximums and minimums, you can read:
brainly.com/question/24701109
GCF is 4a^2
First find the GCF of whole numbers 16 and 12
16: 1, 2, 4, 8, 16
12: 1, 2, 3, 4, 6, 12
Gcf of 16 and 12 is 4
Now a^2 and a^4
Just look at the exponents
The highest you can take out of both of them is a^2
Now put the 4 and a^2 together
Answer is 4a^2
Answer:
96
Step-by-step explanation:
multiply by 12 because thats how many inches are in a foot
Answer:
L = 6, w = 2
Step-by-step explanation:
Let w = width of rectangle
Let L = length of rectangle
w = L - 4
Area of rectangle = Lw
L (L - 4) = 12
L^2 - 4L = 12
L^2 - 4L - 12 = 0
(L - 6)(L + 2) = 0
L - 6 = 0
L = 6 (the other option doesn't work because dimensions can't be negative)
w = L - 4
w = 6 - 4
w = 2
Double check
A = Lw
A = 6 x 2
A = 12
It matches so we are right.
Answer:
Option C) -cosu is correct
Therefore the simplified expression is ![cos(u+\pi)=-cosu](https://tex.z-dn.net/?f=cos%28u%2B%5Cpi%29%3D-cosu)
Step-by-step explanation:
Given expression is ![cos(u+\pi)](https://tex.z-dn.net/?f=cos%28u%2B%5Cpi%29)
To find the value of the given expression :
By using the formula ![cos(A+B)=cosAcosB-sinAsinB](https://tex.z-dn.net/?f=cos%28A%2BB%29%3DcosAcosB-sinAsinB)
Substitute A=u and
in the above formula we get
![cos(u+\pi)=cosucos\pi-sinusin\pi](https://tex.z-dn.net/?f=cos%28u%2B%5Cpi%29%3Dcosucos%5Cpi-sinusin%5Cpi)
( here
and
)
![=-cosu-0](https://tex.z-dn.net/?f=%3D-cosu-0)
![=-cosu](https://tex.z-dn.net/?f=%3D-cosu)
![cos(u+\pi)=-cosu](https://tex.z-dn.net/?f=cos%28u%2B%5Cpi%29%3D-cosu)
Therefore option C) -cosu is correct
Therefore the simplified expression is ![cos(u+\pi)=-cosu](https://tex.z-dn.net/?f=cos%28u%2B%5Cpi%29%3D-cosu)