Minus one half f prime, or the derivative, is equal to zero. Negative one half squared is one fourth, positive one half squared is one fourth. Square root of both sides and you get x is equal to Then what x values is this true at? We just take the plus or minus Divide both sides by four, you get one fourth is equal to x squared. Add four x squared to both sides, you get one is equal to four x squared. One minus four x squared is equal to zero, when does that happen? This one we can just solve. One minus four x squared is equal to zero, let me rewrite that. To be equal to zero is when one minus four x Zero, so the only way we can get f prime of x Things are zero at least one of them has to be Very negative number, you will approach zero but you If you get this exponent to be a really, I guess you could say The product of these twoĮxpressions equalling zero, e to the negative two x squared, that will never be equal to zero. There's no point where this is undefined. Undefined or equal to zero? e to the negative two x squared, this is going to beĭefined for any value of x, this part is going to be defined, and this part is also going toīe defined for any value of x. Negative two x squared times, we have here, one minus four x squared. We're going to have, this is equal to e to the Negative two x squared, I'll do that in green. I'm going to try toįigure out where this is either undefined or where We have that x over there and let's see, can we simplify it at all? Well obviously both of these terms have an e to the negative two x squared. Times negative four x, and of course we have this x over here. That's going to be what, negative four x. We're going to multiply that times the derivative of negative two X squared, well that's just going to be e to the Negative two x squared with respect to negative two That is going to be equal to- We'll just apply the chain rule. Now the derivative of e to the negative two x squared over here. This first part is going to be equal to e to the negative two x squared. What is this going to be? Well all of this stuff in magenta, the derivative of x with respect to x, that's just going to be equal to one. The derivative of e to the negative two x squared Derivative of the x times e to the negative of two x squared plus X squared plus the derivative with respect to x of e to With respect to x of x, so it's going to be that, times e to the negative two We're going to have toĪpply some combination of the product rule and the chain rule. Let's think about how we canįind the derivative of this. The derivative of this with respect to x is either equal Numbers for f we want to figure out all the places where Short for if and only if, f prime of c is equal to zero We would say c is a critical number of f, if and only if. This video and think about, can you find any critical numbers of f. To x times e to the negative two x squared, and we want toįind any critical numbers for f. So it is not considered as a critical point in this case. Apparently x is not a critical point in this case, because when x=3 not only it's derivative h'(3) is undefined but also main function h(3) is also undefined. P.S.: I got it a minute after I submitted the question. It's not just isolated quiz, I did a bunch of them and every time you try to present critical x when f'(x) is undefined it renders my answer incorrect. Yet if you present that both x=3.5 and x=3 are critical number quiz returning answer than 3 is an incorrect answer. Now clearly h'(x) is 0_ when x = 3.5, but also _h'(x) is undefined when x = 3 If you take derivative of that you would get: H(x) = e^2x/(x-3) and a question asking to find critical points. When I'm doing a quiz on Khan Academy I see this: 0:54 Sal mentioned that 'c' is a critical number 'iff' f'(c) = 0 or f'(c) undefined.īut I did few exercises on Khan Academy that ignores points when f'(x) is undefined and states that answer as incorrect.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |