![]() You’ll draw some kind of plane that's tangent right at that point. What you want is the plane that's tangent right at that point. So in this case it actually looks like the graph isĪbout zero at that point so the output of theįunction would be zero. Input point corresponds to such and such a height," Input point you want, you see where that is on the graph, so we go and say, "That Various different spots, it doesn’t have to be where I put it, you could imagine putting Point like this little red dot and that could be at World, move things about, you'll choose some input Sub 0, and then you're gonna find the graph of theįunction that corresponds to just kissing the graphĪt that input point. "What is the input value here?" Maybe you'd name it like x In the single variable world what you might do is say, Like this will be framed if you're trying to find suchĪ tangent plane is first, you think about the specified Say that it will just barely be kissing the graph of thisįunction but at different points. Graph in the one-dimensional circumstance, and it could beĪt various different points rather than just being at that point. That the tangent line just barely kisses the function Just gonna be barely kissing the graph in the same way It's a very two-dimensional surface, instead you’ll have Here, and then instead of having a tangent line,īecause the line is a very one-dimensional thing and here You have some kind of graph of a function, like the one that I have It's actually pretty similar in terms of geometric intuition The function around that point and it turns out to beĪ nice simple approximation. Information how to, let's say you wanted to approximate You’ll find the equationįor that tangent line and this gives you various Given point what the tangent line to that curve is, Is you have some sort of curve and you wanna find at a World a common problem that people like to ask in calculus Of say a parametric surface or something like that but here ![]() Of multivariable calculus you might be taking a tangent plane I'm gonna be talking about tangent planes of graphs,Īnd I'll specify this is tangent planes of graphsĪnd not of some other thing because in different context The section concludes with the extended mean value theorem, which implies Taylor’s theorem.- Hi everyone. ![]() ![]() SECTION 2.5 discusses the approximation of a function \(f\) by the Taylor polynomials of \(f\) and applies this result to locating local extrema of \(f\).SECTION 2.4 presents a comprehensive discussion of L’Hospital’s rule.Topics covered include the interchange of differentiation and arithmetic operations, the chain rule, one-sided derivatives, extreme values of a differentiable function, Rolle’s theorem, the intermediate value theorem for derivatives, and the mean value theorem and its consequences. SECTION 2.3 introduces the derivative and its geometric interpretation.SECTION 2.2 defines continuity and discusses removable discontinuities, composite functions, bounded functions, the intermediate value theorem, uniform continuity, and additional properties of monotonic functions.SECTION 2.1 introduces the concept of function and discusses arithmetic operations on functions, limits, one-sided limits, limits at \(\pm\infty\), and monotonic functions.IN THIS CHAPTER we study the differential calculus of functions of one variable.
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