{"id":165,"date":"2021-07-30T17:24:58","date_gmt":"2021-07-30T17:24:58","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/calculus3\/?post_type=chapter&p=165"},"modified":"2022-10-29T01:51:23","modified_gmt":"2022-10-29T01:51:23","slug":"introduction-to-tangent-planes-and-linear-approximations","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/calculus3\/chapter\/introduction-to-tangent-planes-and-linear-approximations\/","title":{"raw":"Introduction to Tangent Planes and Linear Approximations","rendered":"Introduction to Tangent Planes and Linear Approximations"},"content":{"raw":"In this section, we consider the problem of finding the tangent plane to a surface, which is analogous to finding the equation of a tangent line to a curve when the curve is defined by the graph of a function of one variable, [latex]y=f(x)[\/latex]. The slope of the tangent line at the point [latex]x=a[\/latex] is given by [latex]m=f^{\\prime}(a)[\/latex];\u00a0what is the slope of a tangent plane? We learned about the equation of a plane in\u00a0Equations of Lines and Planes in Space<\/em>; in this section, we see how it can be applied to the problem at hand.","rendered":"

In this section, we consider the problem of finding the tangent plane to a surface, which is analogous to finding the equation of a tangent line to a curve when the curve is defined by the graph of a function of one variable, [latex]y=f(x)[\/latex]. The slope of the tangent line at the point [latex]x=a[\/latex] is given by [latex]m=f^{\\prime}(a)[\/latex];\u00a0what is the slope of a tangent plane? We learned about the equation of a plane in\u00a0Equations of Lines and Planes in Space<\/em>; in this section, we see how it can be applied to the problem at hand.<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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