(a) The curve with equation y2 = 5x4 – x2 is called a kampyle of Eudoxus. Find an equation of the tangent line to this curve at the point (1, 2).
(b) Illustrate part (a) by graphing the curve and the tangent line on a common screen. (If your graphing device will graph implicitly defined curves, then use that capability. If not, you can still graph this curve by graphing its upper and lower halves separately.)
(a)
To find: The equation of the tangent line to the given equation at the point.
Answer to Problem 29E
The equation of the tangent line to the equation
Explanation of Solution
Given:
The curve with equation
The point is
Derivative rules:
(1) Chain rule: If
(2) Product rule: If
Formula used:
The equation of the tangent line at
where, m is the slope of the tangent line at
Calculation:
Obtain the equation of tangent line to the given point.
Differentiate the above equation implicitly with respect to x,
Apply the chain rule (1) and simplify the terms,
Therefore, the derivative of the equation is
The slope of the tangent line at
Thus, the slope of the tangent line at
Substitute
Therefore, the equation of the tangent line to the equation
(b)
To sketch: The curve and tangent line to the given point.
Explanation of Solution
Graph:
Use online graphic calculator to draw the curve and the tangent line as shown below in Figure 1.
From Figure 1, it is observed that the line
Chapter 3 Solutions
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