I'm so happy I teach physics instead of math, now I can say "since you guys already took calculus 1 you know how to take the derivative of this function" and then I look at the practical application of what the derivative represents, e.g. the velocity or whatever.
For fun, after finding slope -29 i used parametric equation: {x = 7 + t {y = - 151 - 29t solve t for x = 0 7 + t = 0 t = - 7 then y = - 151 - 29*(- 7) = 52 (intercept) so tangent is: y= - 29x + 52 😊
This can also easily done by coordinate, slope of a line y = 4a(x-h)^2 is just First we will have to bring equation into above format but after that its really simple yy1 = 2a(x+x1) Since we know y1 and x1, we can simply plug in and while plugging in we can shift the x coordinate by x + h to get the final result
i still don't get it, how did he get y=-29x+150 instead of y=-29x+52 its not like he just forgot the y1 and assumed it was 0 because then it would have been y=-29x+203 so he assumed it was -43 instead of -151? i suppose he calculated (-x)^2 instead of -x^2 cause then it would have been 49-105+3=-(105-52)=-53 and then he also miscalculated that to be -43, or he miscalculated 15*7 to be 95 something like that i guess. so mistake in calculations which is mnemonics problem + wrong sign which is familiarity with notation problem...
I think you're right with the miscalculation of the square, getting 49 instead of -49. And that would be enough, since 203 - 53 is 150. (And as you can see, the difference between 150 and 52 is 98 = 2*49)
why use of "a" AND "x" = not just "x"?!?!?!? I expect more mistakes at the question, I'm at 0:01... I'm sure you will catch them all and overcome them!
I'm so happy I teach physics instead of math, now I can say "since you guys already took calculus 1 you know how to take the derivative of this function" and then I look at the practical application of what the derivative represents, e.g. the velocity or whatever.
Ngl one of my college professors said that science is just math with names/labels attached to it
@@lolidemon3163 bio is applied chem. chem is applied phys. phys is applied maths.
@@lolidemon3163Science is just application of math in the real world
Derivative is just fancy subtraction ;)
@@sohidulislam6020 me in middle school be like: that exists?
0:43 " ... and the direction says: that's the definition of derivative, which is this one right here!"
Me watching in 240p: "yeah I see that!"
😂
Why not just use derivative of f(x) which is -2x-15 put in 7 and slope is -29. Why do the more difficult “h” thing?
The question asks you to do the question using the definition of derivative, So you have to follow the rules,no shortcuts allowed.
For fun, after finding slope -29 i used parametric equation:
{x = 7 + t
{y = - 151 - 29t
solve t for x = 0 7 + t = 0 t = - 7
then y = - 151 - 29*(- 7) = 52 (intercept)
so tangent is: y= - 29x + 52
😊
This can also easily done by coordinate, slope of a line y = 4a(x-h)^2 is just
First we will have to bring equation into above format but after that its really simple
yy1 = 2a(x+x1)
Since we know y1 and x1, we can simply plug in and while plugging in we can shift the x coordinate by x + h to get the final result
Not slope i wanted to say Tanget
The audio for this video is a little out of sync :/
6:03 the **formula** for the tangent line... :)
Audio sync issues again from beginning to around 2:35
Thanks for letting me know!
i still don't get it, how did he get y=-29x+150 instead of y=-29x+52
its not like he just forgot the y1 and assumed it was 0 because then it would have been y=-29x+203
so he assumed it was -43 instead of -151? i suppose he calculated (-x)^2 instead of -x^2 cause then it would have been 49-105+3=-(105-52)=-53 and then he also miscalculated that to be -43, or he miscalculated 15*7 to be 95 something like that i guess. so mistake in calculations which is mnemonics problem + wrong sign which is familiarity with notation problem...
Why -43? If he miscalculated (-x)^2 then he gets -53 and that's what makes it 203-53 = +150
I think you're right with the miscalculation of the square, getting 49 instead of -49. And that would be enough, since 203 - 53 is 150. (And as you can see, the difference between 150 and 52 is 98 = 2*49)
Edit: my mistake, ignore the following (I won't erase because there is a comment correcting me)
2:19 close the outer parentheses! :)
They're already closed. Count again.
@@BigDBrian
you are absolutely correct!
thank you for pointing it out!
Why not use the faster definition for derivatives of d/dx= x^n-1 or whatever it is exactly
it’s not the definition of a derivative. What you just described is the power rule.
@@wistfulgraph yeah but it’s the fastest way to solve derivatives
why use of "a" AND "x" = not just "x"?!?!?!?
I expect more mistakes at the question, I'm at 0:01...
I'm sure you will catch them all and overcome them!
cool!