Find an equation of the tangent line at x 3.
Sketch the line tangent to g (x) at x- 1.57 on the graph above. 1 -2 It is a fact that the derivative of this function is g (x) cosx-x sinx. Understand the physics interpretation of the derivative (as instantaneous velocity). Question: GROUP WORK 1, SECTION 2.2 Tangent Lines and the Derivative Function The following is a graph of g (x)- x cosx. Understand the geometric interpretation of a derivative (as the slope of a tangent line), and be able to use the derivative to help nd the equation of a tangent line. Solution for Tangent Lines and the Derivative Homework Name 2.2 Date Period Problems 1-6 Find lim Find answers to questions asked by students like you. is the fourth derivative.\): The area of the region under the curve is approximated by summing the areas of thin rectangles. 2.2.pdf - LJ Name Tangent Lines and the Derivative Homework Date Period Problems 1- 6 Find Jim f x h - f x Course Hero. Know how to compute the derivative of a function using the limit de nition. Section 2.1 The Derivative and the Tangent Line Problem. We will learn later what these higher order derivatives are used for.
(y double prime) is the third derivative. Is the first derivative of y with respect to x. Example: f(x) = | x |ĥ To be differentiable, a function must be continuous and smooth.ĭerivatives will fail to exist at: corner cusp discontinuity vertical tangent Note: The converse is false: there are functions that are continuous but not differentiable. Theorem: If f is differentiable at a, then f is continuous at a. It is differentiable on an open interval (a,b) if it is differentiable at every number in the interval. dy / dx should not be regarded as a ratio.Ģ The derivative is the slope of the original function.Ī function f is differentiable at a if f ′(a) exists. If we replace number a by a variable x, then the derivative can be interpreted as a function of x : Alternative notations for the derivative: D and d / dx are called differentiation operators. In Section 2.1 we considered the derivative at a fixed number a.
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