Question

here is a graph and the question is , the equation of the first dervative is?

Answer 1

The amplitude is 7, the period is 2pi, so the original function is 7cos(x).
Now, find the derivative of this.

Answer 2

-7sinx??

Answer 3

Yes, good.

Answer 4

The picture is cut off. Upload a fuller picture.

Answer 5

Is the minima at -3?

Answer 6

nope not cut off thats why the dark area still continues

Answer 7

If it is, then the function is 5cos(x) +2.
Now find the derivative of that.

Answer 8

-5sin(x)??

Answer 9

Yeah.

Answer 10

I couldn't see the picture clearly earlier.

Answer 11

how did u do it??

Answer 12

Four things:
1. The cosine function has a maxima at 1 and minima at -1.
2 Since this function does not have -1 and 1, but 7 and -3, it means the cosine was scaled by some number to make it larger.
3. The offset has to make the cosine shift up or down.
4. the function has a period of 2pi. That's just a normal cos(x)
Therefore, a*cos(x) + b

So we have 1(a)+b = 7 (top)
Also -1(a) + b = 3 (bottom)


So you get 2b = 4, b = 2.
Then a = 5.