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Find the point on the graph of f (x) =x?which slope of the tangent = linc...

Question

Find the point on the graph of f (x) =x?which slope of the tangent = linc

Find the point on the graph of f (x) =x? which slope of the tangent = linc



Answers

Find the slope of the tangent line to the graph of $f$ at the given point. Graph $f$ and the tangent line. $$f(x)=3 x^{2}-x \text { at }(0,0)$$

So this time I ask us billions where the slope does not exist of attention lines of this function So we can take derivatives to study those slopes of tangent lines. Girl. So the tooth negative one that come on now, this X will appear in that dominated so it will be under find on X is equal to zero. Well, what does that mean, actually, case see on the side, I look and, like, uh, we have the shirt, Vertical line here I get That's need to know that being undefined in this case represents the sharp cost right here.

They want us to determine the values for which the function doesn't exist, which is derivative doesn't exist. So let's take that area. So we'll have to think it's sometimes one over what's in the cube root of X. And when does this not exist when the denominator is equal to zero? So that's on X is equal to zero. Okay, this is one as a vertical engine, actually, because if we tried to grab that well, we know Ah, the key breed of X looks like it's like this, but it's squared. So we're gonna suddenly bring the left half a board like that. Now let's see if the shooting back down and should all right, good like that. Now, as we get closer into this point, the engine nines go more and more critical, and it corresponds to this little of one. Depart on a graph. Next customer

Okay, so we want to find the equation over attention line. So in order to do that, we're going to need some points on our slope and to find our slope, we can use a dis equation here. So let's start by finding that so we have crime at C where C is our ex points of our point. So that's 81 So that's he quoted a limits as X approaches one of our function and then our function evaluated at one. So this is a negative, too, plus a one. So that's a negative one. So this is equal to positive one here over X minus one. So this gives us the limits as X approaches one, uh, let's see. Um, we contracted us into a negative two x times something and then x times something We went a positive X. So we need this to be a negative one, and there's to be a positive one. So this is all over. X minus one. Actually. See negative two X that's multiplied it out to confirm um and then this is and plus two x squared in minus one very that it's not a square. That's 10 x and we have plus X. No, that should be a minus X show yet minus X and then plus one. Okay, so this is what we want. Okay. And let's cancel out this term and use Jack. Sub two yet Negative. Two times one minus one. So that's equal to make it a three. This here is our slope. You know that We found our slope. It's right that in a point slope form put that in points of form to find the equation of our time line. So this year is equal to y. Minus three is equal to negative three times X minus one. So I'm multiplying through a negative three. We have negative three X plus three. Now, all we have to do is a three to find our equation of our times of mine. Okay, so we got, um this is gonna be why is equal to negative three X plus a six

Hey, guys. And this problem, we're gonna be finding the slope to the line Tangent to the graph f of X equals E to the X at the 0.1 So we can go ahead and take the derivative. The derivative will give us the slope to the line tangent at any given point so we can take the derivative the derivative of either the X is you did the X and I can prove that. So whatever we have the for meat of the U, the derivative is simply eat of the u times. Do you the X We have e to the X take the derivative. That's gonna B e to the x times. Do you d x, the derivative of X is one. So overall we have either the ex. So we're back to our problem. We have you to the X. At 01 we can simply plug in our X value. We don't have to worry about the why, since we're only finding the slope here so we can write DF DX and you can denote it like this. I like to read a line and then at the top xy xy go zero take you to the zero and that is one so we can write m equals one


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