Use the company’s profit equation to determine how many widgets must be made for max profit.

How to solve a quadratic equation word problem about optimization and finding the vertex (max and min).
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[@johnhudelson2652]

I used calculus to determine the answer. I took the first derivative with respect to x and set the derivative to 0 to find the answer.

[@laurendoe168]

Me too :D

[@foxmyx62]

Ditto

[@wtliftr1]

yep, me too- and can do it in your head

[@johnopalko5223]

Yeah, it was a lot simpler to just use calculus. Find the first derivative, set it to zero, and solve for x. You don't even have to write anything down.

[@johnhudelson2652]

@@johnopalko5223 I also solved the problem in my head without writing anything down.

[@terry_willis]

How are we supposed to know that the x value = -b/2a ? I've taken Alg 1 and that was never mentioned.

[@robertlunderwood]

I took Algebra 1 in middle school. Maybe we touched upon it...

[@Kleermaker1000]

My question too. Now it seems as if -b/2a comes out of a high hat. But the same thing goes for finding of the first derivative (f ' (x), in standard form). And why can you find the maximum/vertex by 'saying' f ' (x) = O (in this case: - 2 X + 10 = 0? Those things require proof, in my opinion.

[@b213videoz]

As it turned out I DO know some calculus -2x = - 10 x = 5 I really like this American math tutor guy 😊

[@harrymatabal8448]

You haven't been to south Africa

[@b213videoz]

@@harrymatabal8448 You are right, Ek het niet dort gewees 😁 But I heard much about it.

[@user-kb3it8jf8t]

Alot, your welcome.

[@samjones3106]

pmax = 0 numwidg = 0 for x in range(1000): p = -x**2 + 10*x - 9 if p > pmax: pmax = p numwidg = x print('Number of Widgets = ',numwidg) print('Max profit =', pmax) print("Hello, World!") Number of Widgets = 5 Max profit = 16 Hello, World!

[@DeltaMikeTorrevieja]

So we agree 16 Vs 1600 means teach was only off by a factor of 99, yes?

[@wmfield152]

Great Stuff! Thanks!

[@Kleermaker1000]

Anyone ever had the thought that if 1^0 is 1, then 1^0 = 1^1 so 0 =1? :) Interesting thought, isn't it?

[@gavindeane3670]

1¹ also equals 1² and 1³ and 1⁴ and 1⁵ and... So by your reasoning, pretty much everything equals 1.

[@Kleermaker1000]

@@gavindeane3670 It was only a little joke....

[@russelllomando8460]

That was great. Thanks

[@michaelamato6681]

I recognized that as a negative quadratic, or parabola, the maxima is when the slope is zero.

[@vamsm]

To get the answer, I figured out the vertex of the function which is (5,16).

[@genelowry5666]

Derivative is zero at x=5 hence the answer.

[@danielmadden9691]

5 widgets/day

[@johnnyllooddte3415]

maybe you worded it wrong..but with that equation there is no maximum

[@johnnyllooddte3415]

sorry i didnt see the negative x>2

[@harrymatabal8448]

5.Let me know when you finished talking

[@tonyroland233]

A parabola is not a u shape, you talk nonsense again