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So let's just look at
a quick little example here.

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So I wrote down a function g(w)=5-(w-10)2.

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So let's take the derivative
of this function.

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So we have to go back and
remember our calculus but

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I promise I'll at least
try to keep it simple.

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So the derivative of 5
with respect to w is 0.

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And then the derivative of this term here,
well if you remember, if you have some

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function to some power, well first we drop
that power, that becomes a multiplier.

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We write that function again, and

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the power now is one less than
what the power was before.

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So two minus one is one.

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So I'll just write that
explicitly to the power of one,

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and then I have to multiply by
the derivative of the inside.

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The derivative of this
little function itself.

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So what's the derivative
of w-10 with respect to w.

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It's just 1.

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Okay.

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So, writing this a little bit
more compactly we have -2w

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+ 20 as the derivative.

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And so if we're interested in finding
the maximum of this equation,

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and let me just say how do we know
if we're at a maximum or minimum?

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In both cases we had derivative equals
zero as the solution, well to know if it's

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a min or max, either we can know if we're
looking at a concave or convex function,

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but typically we won't
necessarily know that.

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We can look at the second
derivative of the function.

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Okay, but that's just for
your information.

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You're not gonna need to know that for
this course.

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Okay, so this function, if

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we draw what this function looks like,
then maybe we can see this.

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So we know that at w equals 10,
what's the value of the function?

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It's five.

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So add w=10,
the value of the function is 5 and

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if you go and plot this you'll see that
the value everywhere else is decreasing

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and so it, it has this concave form.

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Okay.

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So, how do I find this maximum?

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Well I take the derivative and
I set it equal to zero and I solve for w.

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So let's do that.

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Let's set derivative = 0.

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So I have -2w + 20 = 0.

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And I solve for w and I get 10.

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Okay, so
that actually matches his picture.

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Indeed, w is 10 at
the maximum of this function.

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