Can someone please explain this to me?
Identify the maximum and minimum values of the function y = 3 cos x in the interval [-2π, 2π]. Use your understanding of transformations, not your graphing calculator.

Question

Can someone please explain this to me?
Identify the maximum and minimum values of the function y = 3 cos x in the interval [-2π, 2π]. Use your understanding of transformations, not your graphing calculator.

anonymous · Answer

Do you know the minimum and maximum values of  $y=\cos x$ over the interval $[-2\pi,2\pi]$?

anonymous · Answer

Honestly, I don't even understand what it's asking for. What does it mean by the interval [-2pi, 2pi]?

anonymous · Answer

$-2\pi \leq x \leq 2\pi$
i.e. $x$ is between $-2\pi$ and $2\pi$

anonymous · Answer

Okay, that means on a graph. Do the signs always go that way? 
$$-->  \le $$

anonymous · Answer

@mathmale

anonymous · Answer

you could write it
$$2\pi \geq x \geq -2\pi$$
as long as it means "in between"

anonymous · Answer

Oh, okay. I gotcha. So how do find what you said? y= cos x?

anonymous · Answer

Well, you could try putting in values of x or drawing it or, the most general method of finding minima or maxima of a function $f(x)$ is to differentiate and set to zero
$$\frac{\text{d}f}{\text{d}x} = 0$$
so solving  $-\sin x = 0$ will give you values for $x$ for which $\cos x$ is maximum

mathmale · Answer

BG:  I think you'd find it very helpful to actually graph y = 3 cos x on the given interval.  From the graph it'd be immediately evident that this function has more than one max and more than one min within that interval.

You cool with graphing the cosine function y=cos x?  y=3cos x?

anonymous · Answer

Hold on a minute, MM. I will do that afterwards. I have to explain how I found my answer without the use of a calculator, but I'd love the tips on how to do this more easily afterwards! :)

mathmale · Answer

Broken Symm's most recent statement is helpful and accurate.  But I'd still suggest graphing the function y=3cos x on [-2pi,2pi].

anonymous · Answer

What is d in that equation?

anonymous · Answer

*maximum or minimum
I should have said

mathmale · Answer

I'm going to graph y=cos x on [0,2p] quickly.  We really need to know by heart the shapes of the graphs of sin x, cos x and tan x, so that no calculator is needed to graph them.

anonymous · Answer

oh, $$\frac{\text{d}}{\text{d}x}$$ is an operator

Have you done any calculus?

anonymous · Answer

Nope. That's the class I'm in. Haha.

anonymous · Answer

attachment

anonymous · Answer

Was that d/dx?

mathmale · Answer

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