What is the parametric form for the tangent line to y = 2x^(2)+2x-1 at x = -1?

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To find the parametric form of the tangent line to the curve y = 2x^2 + 2x - 1 at x = -1, first calculate the slope of the tangent line, which is -2. The point on the tangent line at x = -1 is (-1, -1). The equation of the tangent line is y = -2x - 3. To express this in parametric form, set x = t, resulting in y = -2t - 3. The final parametric equations are x = t and y = -2t - 3.
Loppyfoot
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Homework Statement



The parametric form for the tangent line to the graph of y = 2x^(2)+2x-1 at x = -1 is

Homework Equations





The Attempt at a Solution



I am confused about where to begin this problem. Any thoughts?

Thanks!
 
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Loppyfoot said:

Homework Statement



The parametric form for the tangent line to the graph of y = 2x^(2)+2x-1 at x = -1 is

Homework Equations





The Attempt at a Solution



I am confused about where to begin this problem. Any thoughts?

Thanks!
The first step would be to find the slope of the tangent line at the point (-1, f(-1)). Once you have the slope of the tangent line, and a point on the tangent line - (-1, f(-1)), you can find the equation of the tangent line.

The final step would be to write the equation of the tangent line in parametric form.
 
So the slope of the tangent line would be:

y'=4x+2...plug in x=-1.

slope of tangent line at x=-1 is y'=-2.

A point on the line would be (-1,-1).

How would I translate this data into parametric form
 
You skipped a step - you need to find the equation of the tangent line first.
 
so the equation of the tangent line is y=-2x-3.


How would I translate the y=mx+b into the parametric form?
 
Let x = t. Then you have y = -2t - 3, x = t.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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