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Given the quadratic function in blue and the line tangent to the curve at A in red, move point A and investigate what happens to the gradient of the tangent line. O O Conic c: y = x²-x-2 Line a: -0.5x + 0.5y = Number b = 1 Point A = (1, -2) .♡ -2 6 5 4 3 2 1 0 -1 -2 -3 a A 1 b=1 3 4 5

Given the quadratic function in blue and the line tangent to the curve at A in red, move point A and investigate what happens to the gradient of the tangent line. O O Conic c: y = x²-x-2 Line a: -0.5x + 0.5y = Number b = 1 Point A = (1, -2) .♡ -2 6 5 4 3 2 1 0 -1 -2 -3 a A 1 b=1 3 4 5

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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Given the quadratic function in blue and the line tangent to the curve at A in red, move point A and investigate what happens to the gradient of the tangent line. Conic c: y = x²-x-2 Line a: -0.5x + 0.5y Number b = 1 Point A = (1, -2) || -4 -3 -2 6 5 4 m 3 2 1 0 -2 -3 a A 1 /2 b=1 3 4 5 6
Transcribed Image Text:Given the quadratic function in blue and the line tangent to the curve at A in red, move point A and investigate what happens to the gradient of the tangent line. Conic c: y = x²-x-2 Line a: -0.5x + 0.5y Number b = 1 Point A = (1, -2) || -4 -3 -2 6 5 4 m 3 2 1 0 -2 -3 a A 1 /2 b=1 3 4 5 6
Experiment 3: Slide the blue circle on the parabola to the point where the tangent line is exactly horizontal. 3A. Does the slope of the tangent line appear to be positive, negative, zero or undefined? 3B. State the slope of the tangent line as an integer. 3C. The equation of the parabola is f(x) = x^2 - x - 2. Calculate the derivative f'(x). Evaluate f'(1) and state its value. 3D. Compare the slope rise/run to f'(1). How did they compare? Were they the same or different?
Transcribed Image Text:Experiment 3: Slide the blue circle on the parabola to the point where the tangent line is exactly horizontal. 3A. Does the slope of the tangent line appear to be positive, negative, zero or undefined? 3B. State the slope of the tangent line as an integer. 3C. The equation of the parabola is f(x) = x^2 - x - 2. Calculate the derivative f'(x). Evaluate f'(1) and state its value. 3D. Compare the slope rise/run to f'(1). How did they compare? Were they the same or different?
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