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2) At what point(s) will the tangent line to y = x² – 4x + 3 be horizontal?

2) At what point(s) will the tangent line to y = x² – 4x + 3 be horizontal?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Computational: Answer only no.2 and Analysis: Real-Life Applications no.3 only (a,b)
PERFORMANCE TASK NO. 3 Title: Limit Definition of Derivative and the Tangent Line Tasks: Solve the following problems completely and accurately. Use the limit definition of derivative. Computational: (1) Given the function y = x³ + 3x + 1, answer the following items. a) Find the slope of the tangent line at the point (0,1). b) Find the equation of the tangent line at the point (0,1). Verify your answer by showing the graph of the function and the tangent line at the given point. Find all points at which the slope of the tangent line to the given function c) equals 5. (2) At what point(s) will the tangent line to y = x² – 4x + 3 be horizontal? (3) Find an equation of the tangent line to the curve y = 2x² + 3 that is parallel to the line 8x - y+ 3 = 0.
Transcribed Image Text:PERFORMANCE TASK NO. 3 Title: Limit Definition of Derivative and the Tangent Line Tasks: Solve the following problems completely and accurately. Use the limit definition of derivative. Computational: (1) Given the function y = x³ + 3x + 1, answer the following items. a) Find the slope of the tangent line at the point (0,1). b) Find the equation of the tangent line at the point (0,1). Verify your answer by showing the graph of the function and the tangent line at the given point. Find all points at which the slope of the tangent line to the given function c) equals 5. (2) At what point(s) will the tangent line to y = x² – 4x + 3 be horizontal? (3) Find an equation of the tangent line to the curve y = 2x² + 3 that is parallel to the line 8x - y+ 3 = 0.
Analysis: Real-life Applications Derivative is defined as the rate of change of a function with respect to a variable. (1) The number of organisms of a certain bacteria at time t can be modeled according to the function N(t) = 2500(1 + 2t?). %3D Find the rate of change of the number. (2) A buko pie store can produce buko pie at Php95.00. It is estimated that if the selling price of the buko pie is x pesos, then the number of buko pie sold each day is 1000 – x. a) Express the daily profit of the store as a function of x. b) Find the derivative of the function formed in part (a). Hint: Profit = Revenue - Cost (3) A wire 10 cm long is cut into two pieces, one of length x and the other of length 10 – x. Each is bent in a shape of a square. a) Find a function that models the total area enclosed by the two squares as a function of x. b) Find the derivative of the function formed in part (a).
Transcribed Image Text:Analysis: Real-life Applications Derivative is defined as the rate of change of a function with respect to a variable. (1) The number of organisms of a certain bacteria at time t can be modeled according to the function N(t) = 2500(1 + 2t?). %3D Find the rate of change of the number. (2) A buko pie store can produce buko pie at Php95.00. It is estimated that if the selling price of the buko pie is x pesos, then the number of buko pie sold each day is 1000 – x. a) Express the daily profit of the store as a function of x. b) Find the derivative of the function formed in part (a). Hint: Profit = Revenue - Cost (3) A wire 10 cm long is cut into two pieces, one of length x and the other of length 10 – x. Each is bent in a shape of a square. a) Find a function that models the total area enclosed by the two squares as a function of x. b) Find the derivative of the function formed in part (a).
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