2. Consider the function f(x) = 4 – x2. (a) Draw a sketch of the graph of the function. (b) Find the slope of the secant line connecting the points P(1,3) and Q(2,0) on the graph. (c) Find the slope of the secant line connecting the points P(1,3) and Q(x, 4 – x²). (d) Use algebra to simplify your formula from part (c) as much as possible, assuming that P and Q are distinct points. (e) What value do you get when you plug x = 1 into the simplified expression you found in part (d)? (f) Assume that your answer in part (e) is the slope of the tangent line to the graph y = 4 – x2 at the point P(1,3). Use that information to write an equation for the tangent line to the graph y = 4 – x² at the point P(1,3).
2. Consider the function f(x) = 4 – x2. (a) Draw a sketch of the graph of the function. (b) Find the slope of the secant line connecting the points P(1,3) and Q(2,0) on the graph. (c) Find the slope of the secant line connecting the points P(1,3) and Q(x, 4 – x²). (d) Use algebra to simplify your formula from part (c) as much as possible, assuming that P and Q are distinct points. (e) What value do you get when you plug x = 1 into the simplified expression you found in part (d)? (f) Assume that your answer in part (e) is the slope of the tangent line to the graph y = 4 – x2 at the point P(1,3). Use that information to write an equation for the tangent line to the graph y = 4 – x² at the point P(1,3).
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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Transcribed Image Text:2. Consider the function f(x) = 4 – x².
(a) Draw a sketch of the graph of the function.
(b) Find the slope of the secant line connecting the points P(1, 3) and Q(2,0) on the
graph.
(c) Find the slope of the secant line connecting the points P(1,3) and Q(x,4 – x²).
(d) Use algebra to simplify your formula from part (c) as much as possible, assuming
that P and Q are distinct points.
(e) What value do you get when you plug x = 1 into the simplified expression you found
in part (d)?
(f) Assume that your answer in part (e) is the slope of the tangent line to the graph
y = 4 – x2 at the point P(1,3). Use that information to write an equation for the
tangent line to the graph y = 4 – a² at the point P(1,3).
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