2.2 tangent lines and the derivative homework

What happens to the rate at which the percentage is growing as more years go by?Īs more years go by, the change in percentage grows at a slower rate. The percent of mothers returning to the work force increased on average. is the fourth derivative.Calculate the slope of the secant line for each of the following intervals for the function $f(x) =. 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. b) Find the equation of the tangent line to the graph of the function for. Theorem: If f is differentiable at a, then f is continuous at a. Section 2.2 Derivatives of Products and Quotients (Minimum Homework: all odds). It is differentiable on an open interval (a,b) if it is differentiable at every number in the interval. 26) Finding Equation of Tangent Line to Square Root Function 27) Slope of Square Root Function, Example 2 28) Slope of Square Root Function at Any x 29) Existence of Tangent Line, Part I 30) Existence of Tangent Line, Part II 31) Existence of Tangent Line, Part III 32) Slope of a Piecewise-Defined Function 33) The Derivative and its. 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.

2.2 tangent lines and the derivative homework