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Think About It In Exercises 53–56, sketch the graph of a function f having the given characteristics.
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Calculus of a Single Variable
- Determine whether the function is increasing, decreasing, or neither: I+ z* (d) g(t) = 13 +t (a) f(x)= 3¬* (b) f(x) = x2 + 1 (c) g(t) = t2 + tarrow_forwardThis question is about the function f(x) = x + (6/x)arrow_forwardUse the definition of the derivative to find the equations of the lines described in Exercises 59–64. 59. The tangent line to f(x) = x² at x = -3. 60. The tangent line to f(x) = x² at x = 0. 61. The line tangent to the graph of y = 1 – x – x² at the point (1, –1). 62. The line tangent to the graph of y = 4x + 3 at the point (-2, –5). %3D 63. The line that passes through the point (3, 2) and is parallel to the tangent line to f(x) = - at x = -1. 64. The line that is perpendicular to the tangent line to f (x) = x4 +1 at x = 2 and also passes through the point (–1, 8). For each function f graphed in Exercises 65–68, determine the values of x at which f fails to be continuous and/or differen- tiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.arrow_forward
- Identify the equation that defines y as a function of x (a) x+(y- 1)² = 3 (b) x2-y = 3xy (c) 3x+ 5y = 1 (d) x*+y* = 1 Select one: (d) O (b) (c) O (a)arrow_forwardIn Exercises 29–42, use the ProductRule or the Quotient Rule to find the derivative of the function.29. f (x) = (5x2 + 8)(x2 − 4x − 6)arrow_forwardConsider the function F(x)= (x+2)^2 for the domain [-2, ∞)arrow_forward
- In Exercises 67–73, estimate derivatives using the symmetric difference quotient (SDQ), defined as the average of the difference quotients at h and -h: 1(f(a + h) – f(a) f (a – h) – f(a) -h f (a + h) – f(a – h) | 1 2h The SDQ usually gives a better approximation to the derivative than the difference quotient. 67. The vapor pressure of water at temperature T (in kelvins) is the atmospheric pressure P at which no net evaporation takes place. Use the following table to estimate P'(T) for T = 303, 313, 323, 333, 343 by computing the SDQ given by Eq. (1) with h = 10. т (К) 293 303 313 323 333 343 353 P (atm) 0.0278 0.0482 0.0808 0.1311 0.2067 0.3173 0.4754arrow_forwardA right triangle has one vertex on the graph of y = x3, x > 0, at (x, y) another at the origin, and the third on the positive y-axis at (0, y). Express the area A of the triangle as a function of x.arrow_forwardlet H(x)(1+x^2)^3. find f and g such that f(g(x))=H(x)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,