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4. Consider the parametric curve given by x(t) = -7t and y(t) = −3t². (a) Sketch this curve on the interval −2 ≤ t ≤ 2 and indicate its orientation. (b) Find the equation of the tangent line to the curve at t = 1.

4. Consider the parametric curve given by x(t) = -7t and y(t) = −3t². (a) Sketch this curve on the interval −2 ≤ t ≤ 2 and indicate its orientation. (b) Find the equation of the tangent line to the curve at t = 1.

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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**Problem 4: Parametric Curve Analysis** Consider the parametric curve given by \( x(t) = -7t \) and \( y(t) = -3t^2 \). **(a)** Sketch this curve on the interval \(-2 \leq t \leq 2\) and indicate its orientation. - To sketch the curve, calculate the coordinates \((x, y)\) for selected values of \(t\) within the interval. Use these points to plot the curve on a graph, showing how it progresses with increasing \(t\). **(b)** Find the equation of the tangent line to the curve at \(t = 1\). - To find the equation of the tangent line, first determine the derivatives \(x'(t)\) and \(y'(t)\). Use \(t = 1\) to find the slope of the tangent. - The formula for the tangent line at \(t = 1\) involves plugging in the values of \(x(1)\) and \(y(1)\) and using the point-slope form of a line.
Transcribed Image Text:**Problem 4: Parametric Curve Analysis** Consider the parametric curve given by \( x(t) = -7t \) and \( y(t) = -3t^2 \). **(a)** Sketch this curve on the interval \(-2 \leq t \leq 2\) and indicate its orientation. - To sketch the curve, calculate the coordinates \((x, y)\) for selected values of \(t\) within the interval. Use these points to plot the curve on a graph, showing how it progresses with increasing \(t\). **(b)** Find the equation of the tangent line to the curve at \(t = 1\). - To find the equation of the tangent line, first determine the derivatives \(x'(t)\) and \(y'(t)\). Use \(t = 1\) to find the slope of the tangent. - The formula for the tangent line at \(t = 1\) involves plugging in the values of \(x(1)\) and \(y(1)\) and using the point-slope form of a line.
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