 2.2.1: The function f (x) is defined by the formulaf (x) = limh0
 2.2.2: (a) The derivative of f(x) = x2 is f (x) = .(b) The derivative of f...
 2.2.3: Suppose that the line 2x + 3y = 5 is tangent to the graphof y = f(x...
 2.2.4: Which theorem guarantees us that iflimh0f(x0 + h) f(x0)hexists, the...
 2.2.5: Sketch the graph of a function f for which f(0) = 1,f (0) = 0, f (x...
 2.2.6: Sketch the graph of a function f for which f(0) = 0,f (0) = 0, and ...
 2.2.7: Given that f(3) = 1 and f (3) = 5, find an equation forthe tangent ...
 2.2.8: Given that f(2) = 3 and f (2) = 4, find an equationfor the tangent ...
 2.2.9: 914 Use Definition 2.2.1 to find f (x), and then find the tangent l...
 2.2.10: 914 Use Definition 2.2.1 to find f (x), and then find the tangent l...
 2.2.11: 914 Use Definition 2.2.1 to find f (x), and then find the tangent l...
 2.2.12: 914 Use Definition 2.2.1 to find f (x), and then find the tangent l...
 2.2.13: 914 Use Definition 2.2.1 to find f (x), and then find the tangent l...
 2.2.14: 914 Use Definition 2.2.1 to find f (x), and then find the tangent l...
 2.2.15: 1520 Use Formula (12) to find dy/dx. y = 1x
 2.2.16: 1520 Use Formula (12) to find dy/dx. y = 1x + 1
 2.2.17: 1520 Use Formula (12) to find dy/dx. y = x2 x
 2.2.18: 1520 Use Formula (12) to find dy/dx. y = x4
 2.2.19: 1520 Use Formula (12) to find dy/dx. y = 1x
 2.2.20: 1520 Use Formula (12) to find dy/dx. y = 1x 1
 2.2.21: 2122 Use Definition 2.2.1 (with appropriate change in notation) to ...
 2.2.22: 2122 Use Definition 2.2.1 (with appropriate change in notation) to ...
 2.2.23: Match the graphs of the functions shown in (a)(f ) with the graphs ...
 2.2.24: Let f(x) = 1 x2. Use a geometric argument to findf (2/2).
 2.2.25: 2526 Sketch the graph of the derivative of the function whose graph...
 2.2.26: 2526 Sketch the graph of the derivative of the function whose graph...
 2.2.27: 2730 TrueFalse Determine whether the statement is true or false. Ex...
 2.2.28: 2730 TrueFalse Determine whether the statement is true or false. Ex...
 2.2.29: 2730 TrueFalse Determine whether the statement is true or false. Ex...
 2.2.30: 2730 TrueFalse Determine whether the statement is true or false. Ex...
 2.2.31: 3132 The given limit represents f (a) for some function f and some ...
 2.2.32: 3132 The given limit represents f (a) for some function f and some ...
 2.2.33: Find dy/dxx=1, given that y = 1 x2.
 2.2.34: Find dy/dxx=2, given that y = (x + 2)/x.
 2.2.35: Find an equation for the line that is tangent to the curvey = x3 2x...
 2.2.36: Use a graphing utility to graph the following on the samescreen: th...
 2.2.37: Let f(x) = 2x . Estimate f (1) by(a) using a graphing utility to zo...
 2.2.38: Let f(x) = sin x. Estimate f (/4) by(a) using a graphing utility to...
 2.2.39: 3940 The function f whose graph is shown below has values as given ...
 2.2.40: 3940 The function f whose graph is shown below has values as given ...
 2.2.41: Suppose that the cost of drilling x feet for an oil well isC = f(x)...
 2.2.42: A paint manufacturing company estimates that it cansell g = f(p) ga...
 2.2.43: It is a fact that when a flexible rope is wrapped arounda rough cyl...
 2.2.44: The accompanying figure shows the velocity versus timecurve for a r...
 2.2.45: According to Newtons Law of Cooling, the rate ofchange of an object...
 2.2.46: Show that f(x) is continuous but not differentiable at theindicated...
 2.2.47: Show thatf(x) =x2 + 1, x 12x, x > 1is continuous and differentiable...
 2.2.48: Show thatf(x) =x2 + 2, x 1x + 2, x> 1is continuous but not differen...
 2.2.49: Show thatf(x) =x sin(1/x), x = 00, x = 0is continuous but not diffe...
 2.2.50: . Show thatf(x) =x2 sin(1/x), x = 00, x = 0is continuous and differ...
 2.2.51: Suppose that a function f is differentiable at x0 and thatf (x0) > ...
 2.2.52: Suppose that a function f is differentiable at x0 and defineg(x) = ...
 2.2.53: Suppose that a function f is differentiable at x = 0 withf(0) = f (...
 2.2.54: Suppose that f is differentiable at x0. Modify the argumentof Exerc...
 2.2.55: Writing Write a paragraph that explains what it means for afunction...
 2.2.56: Writing Explain the relationship between continuity anddifferentiab...
Solutions for Chapter 2.2: THE DERIVATIVE FUNCTION
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 2.2: THE DERIVATIVE FUNCTION
Get Full SolutionsCalculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. Since 56 problems in chapter 2.2: THE DERIVATIVE FUNCTION have been answered, more than 40053 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.2: THE DERIVATIVE FUNCTION includes 56 full stepbystep solutions.

Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

Causation
A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable

Commutative properties
a + b = b + a ab = ba

Coterminal angles
Two angles having the same initial side and the same terminal side

Equal matrices
Matrices that have the same order and equal corresponding elements.

equation of a quadratic function
ƒ(x) = ax 2 + bx + c(a ? 0)

Identity properties
a + 0 = a, a ? 1 = a

Logarithmic reexpression of data
Transformation of a data set involving the natural logarithm: exponential regression, natural logarithmic regression, power regression

Natural logarithmic function
The inverse of the exponential function y = ex, denoted by y = ln x.

Nautical mile
Length of 1 minute of arc along the Earth’s equator.

nth power of a
The number with n factors of a , where n is the exponent and a is the base.

Permutations of n objects taken r at a time
There are nPr = n!1n  r2! such permutations

Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.

Polar coordinates
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle

Polynomial in x
An expression that can be written in the form an x n + an1x n1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)

Power regression
A procedure for fitting a curve y = a . x b to a set of data.

Quotient identities
tan ?= sin ?cos ?and cot ?= cos ? sin ?

Radian measure
The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.

Relation
A set of ordered pairs of real numbers.

Stem
The initial digit or digits of a number in a stemplot.