The download contains the complete GBW32 V5.0 software package. You may have to disable your antivirus software. The software runs complete but is unregistered. If you continue to use the software please register your copy. Run the Help file for registration information or click on the Register GBW32 button. You may copy and distribute the. ![]() Tips for better search results • Ensure correct spelling and spacing - Examples: 'paper jam' • Use product model name: - Examples: laserjet pro p1102, DeskJet 2130 • For HP products a product number. - Examples: LG534UA • For Samsung Print products, enter the M/C or Model Code found on the product label. - Examples: “SL-M2020W/XAA” • Include keywords along with product name. Examples: 'LaserJet Pro P1102 paper jam', 'EliteBook 840 G3 bios update' Need help finding your product name or product number? This product detection tool installs software on your Microsoft Windows device that allows HP to detect and gather data about your HP and Compaq products to provide quick access to support information and solutions. Technical data is gathered for the products supported by this tool and is used to identify products, provide relevant solutions and automatically update this tool, to improve our products, solutions, services, and your experience as our customer. Note: This tool applies to Microsoft Windows PC's only. This tool will detect HP PCs and HP printers. This product detection tool installs software on your Microsoft Windows device that allows HP to detect and gather data about your HP and Compaq products to provide quick access to support information and solutions. Technical data is gathered for the products supported by this tool and is used to identify products, provide relevant solutions and automatically update this tool, to improve our products, solutions, services, and your experience as our customer. Note: This tool applies to Microsoft Windows PC's only. This tool will detect HP PCs and HP printers. First, Second Derivatives and Graphs of Functions A tutorial on how to use the first and second derivatives, in, to study the properties of the graphs of functions. To graph functions in calculus we first review several theorem. 3 theorems have been used to find maxima and minima and they will be used to graph functions. We need 2 more theorems to be able to study the graphs of functions using first and second derivatives. Theorem 4: If f is differentiable on an interval (I1, I2) and differentiable on [I1, I2] and 4.a - If f ' (x) > 0 on (I1, I2), then f is increasing on [I1, I2]. 4.b - If f ' (x) 0 on (I1, I2), then f has concavity up on [I1, I2]. Activation code for driver talent pro. 5.b - If f ' (x). Example 1: Use first and second derivative theorems to graph function f defined by f(x) = x 2 Solution to Example 1. Step 1: Find the first derivative, any stationary points and the sign of f ' (x) to find intervals where f increases or decreases. F ' (x) = 2x The stationary points are solutions to: f ' (x) = 2x = 0, which gives x = 0. The sign of f ' (x) is given in the table below. F ' (x) is negative on (-∞, 0) f decreases on this interval. F ' (x) is positive on (0, ∞) f increases on this interval. Also according to theorem 2(part a), f has a minimum at x = 0. Step 2: Find the second derivative, its signs and any information about concavity. F '(x) = 2 and is always positive (this confirms the fact that f has a minimum value at x = 0 since f '(0) = 2, theorem 3(part a)), the graph of f will be concave up on (-∞, +∞) according to theorem 5(part a) above. Step 3: Find any x and y intercepts and extrema. Y intercept = f(0) = 0. X intercepts are found by solving f(x) = x 2 = 0. X intercept = 0. From the signs of f ' and f', there is a minimum at x = 0 which gives the minimum point at (0, 0). Step 4: Put all information in a table and graph f. Also as x becomes very large (+∞) or veyy small (-∞), f(x) = x 2 becomes very large. See table above and graph below. Example 2: Use first and second derivative theorems to graph function f defined by f(x) = x 3 - 4x 2 + 4x Solution to Example 2. Step 1: f ' (x) = 3x 2 - 8x + 4. Solve 3x 2 - 8x + 4 = 0 solutions are: x = 2 and x = 2/3, see table of sign below that also shows interval of increase/decrease and maximum and minimum points. Step 2: f ' (x) = 6x - 8. Solve 6x - 8 = 0; solution is x = 4/3 inflection point: where concavity changes. See sign and concavity in table below. Step 3: y intercept = f(0) = 0. X intercepts solve x 3 - 4x 2 + 4x = 0. Factor x out x(x 2 - 4x + 4) = 0 and solve the quadratic equation x 2 - 4x + 4 = (x - 2) 2 = 0 to find solutions: x = 0, x = 2 of multiplicity 2. Also as x becomes very large (+∞), f(x) = x 3 - 4x 2 + 4x becomes very large (+∞).
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