In this chapter, we will study applications of the derivative in various Further, if two variables x and y are varying with respect to another variable
The angle of intersection between two curves is the angle between the tangents to the curves at the point of intersection 6 1 3 Approximation Since f ?(x) = 0
This is frequently the case, but often the two variables are related in some way so that “really” there is only one variable So our next step is to find the
3 5 The Derivatives of and 3 6 An Economics Application: Elasticity of Demand loga x ax Why It's Important In this chapter, we consider two types of
All our applications will center on what economists call the theory of the firm In other words, we study The first two derivatives of C(x) are given by
Suppose f and g be two real function continuous at a real number c then Basic application of derivatives in finding marginal cost, marginal revenues :
of intersection of two lines 2 Conic sections Applications of Derivatives rate of change of bodies, use of derivatives in approximation
Between any two roots of a polynomial f(x), there is always a root of its derivative f' (x) Lagrange's Mean Value Theorem Let f be a real function, continuous
Applications of the Derivative Inverse Functions and Their Derivatives becomes u(x) times dvldx-we can multiply the two limits-plus v(x) times duldx
equations by examples, solving system of linear equations in two or three Applications of derivatives: rate of change of bodies,
In this chapter, we will study applications of the derivative in various Further, if two variables x and y are varying with respect to another variable t, i e , if ( ) x f t
In this chapter we use derivatives to find extreme values of functions, to determine and analyze the absolute maximum) may occur at two or more different points of the interval Graph the volume of a 108-in box (length plus girth equals
of intersection of two lines 2 Conic sections Unit-IV : Calculus 1 Limits and Derivatives Nil rate of change of bodies, use of derivatives in approximation
2 4 Using Derivatives to Find Absolute Maximum and Minimum introduction in Section R 5 of two apps for the iPhone: iPlot and Graphicus These are culators like the TI-83 Plus and the TI-84 Plus do, they are accessibly priced and visually