Parallel Tangent Line on y=2-e^x+4x and 2x+y=5?

Thread starter ttpp1124
Start date May 12, 2020
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Curve Line Parallel Point Tangent Tangent line

In summary, the equation of the tangent line at the point of tangency is y = 4x + 3. The point of tangency can be found by setting the derivative of the curve equal to the slope of the given line and solving for the x-value. The slope of the tangent line at the point of tangency is 4. If the slope of the tangent line is equal to the slope of the given line, then the tangent line is parallel to the given line. The value of e affects the point of tangency by changing the x-coordinate of the point, with a higher value of e causing a left shift and a lower value of e causing a right shift.

May 12, 2020

ttpp1124

Homework Statement: can someone check my work, please?

Relevant Equations: n/a

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May 12, 2020

etotheipi

Yep

1. What is a parallel tangent line?

A parallel tangent line is a line that runs parallel to a given curve and touches the curve at only one point, known as the point of tangency. This means that the slope of the tangent line is equal to the slope of the curve at that point.

2. How do you find a parallel tangent line on a given curve?

To find a parallel tangent line on a given curve, you first need to find the slope of the curve at the point of tangency. This can be done by taking the derivative of the curve at that point. Then, using the slope and the given point of tangency, you can use the point-slope formula to find the equation of the parallel tangent line.

3. What is the equation of the parallel tangent line on y=2-e^x+4x and 2x+y=5?

The equation of the parallel tangent line on y=2-e^x+4x and 2x+y=5 is y = 4x + 1. This can be found by taking the derivative of y=2-e^x+4x, which is 4-e^x, and setting it equal to the slope of the parallel tangent line, which is 4. Then, using the point-slope formula with the given point of tangency (2,5), the equation of the parallel tangent line can be found.

4. How do you know if two lines are parallel?

Two lines are parallel if they have the same slope. This means that they will never intersect and will always be the same distance apart.

5. Can a curve have more than one parallel tangent line?

No, a curve can only have one parallel tangent line at a given point. This is because the slope of the tangent line is determined by the slope of the curve at that point, and the slope of a curve can only have one value at a given point.