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Use the product, quotient, power, and or chain rule to differentiate. 1) y= ( 5x2 -4x +7)(9x²-8)

Use the product, quotient, power, and or chain rule to differentiate. 1) y= ( 5x2 -4x +7)(9x²-8)

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.3: Polynomial Equations
Problem 46PS
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Use the product, quotient, power, and or chain rule to differentiate. 1) y= ( 5x2-4x +7)(9x²-8) x3-2x+9 2) y = x2-4 3) y = -7 (3x4 – 5x² + 9)² 4) y = (4x + 7)$ (6 – 3x)* d3y find 3 5) If y = 4x3 + at dx3 6) If f(x) = V2x find f"(x) and f"(4) 14 7) If f(x) = - find f"(x) (4x-5)2 8) Find the equation of the line tangent to the graph of f(x) = x - at the point where x = 1. 9) Find the point(s), if any, where the graph has a horizontal tangent for 3x4 3x2 f(x) 4 2 10) Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cm3 /s. How fast is the radius the balloon increasing when the diameter is 50 cm? A company that manufactures sport supplements calculates that its costs and 11) demand functions can be modeled by the equations C = 125,000 + .75x and he p = 250 – 10* -x where x is the number of units of sport supplements produced in 1 week. If production in one particular week is 1,000 units and is increasing at a rate of 150 units per week, find the rate at which the profit is increasing.
Transcribed Image Text:Use the product, quotient, power, and or chain rule to differentiate. 1) y= ( 5x2-4x +7)(9x²-8) x3-2x+9 2) y = x2-4 3) y = -7 (3x4 – 5x² + 9)² 4) y = (4x + 7)$ (6 – 3x)* d3y find 3 5) If y = 4x3 + at dx3 6) If f(x) = V2x find f"(x) and f"(4) 14 7) If f(x) = - find f"(x) (4x-5)2 8) Find the equation of the line tangent to the graph of f(x) = x - at the point where x = 1. 9) Find the point(s), if any, where the graph has a horizontal tangent for 3x4 3x2 f(x) 4 2 10) Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cm3 /s. How fast is the radius the balloon increasing when the diameter is 50 cm? A company that manufactures sport supplements calculates that its costs and 11) demand functions can be modeled by the equations C = 125,000 + .75x and he p = 250 – 10* -x where x is the number of units of sport supplements produced in 1 week. If production in one particular week is 1,000 units and is increasing at a rate of 150 units per week, find the rate at which the profit is increasing.
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