Finding the Perpendicular Tangent on a Parabola

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In summary, the conversation discusses finding the slope of the tangent to the parabola y=-3x^2 + 4x - 7 at x=a and determining the value of a where the tangent is perpendicular to the line 3x - 4y + 8=0. The derivative of the parabola is used to find the slope and the expression 6x + 4 is set equal to -4/3 to solve for the value of a.
  • #1
emma3001
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Find the slope of the tangent to the parabola y=-3x^2 + 4x - 7 when x=a. I know how to get the limit using the tangent so i end up with a slope in terms of a (you can also get it using the derivative) but now the next part states:
At what point on the parabola is the tangent perpendicular to the line 3x - 4y + 8=0 and all that i get from that question is that the tangent for the point on the parabola will have a slope of -4/3 (negative reciprocal)
 
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  • #2
so you have the derivative in terms of a, right? Let's call it D(a).

You're looking for the value for a such that this expression is equal to -4/3.

So what about solving D(a)=-4/3 for a ..?
 
  • #3
sorry... so if the derivative is 6x + 4, then i can say that 6x + 4= -4/3 and solve for a (or x)?
 
  • #4
Exactly, sometimes it's easier than you think :smile:
 

What is the definition of slope of a tangent?

The slope of a tangent is the rate of change of a curve at a specific point. In other words, it is the instantaneous rate of change or the steepness of a curve at a particular point.

How is the slope of a tangent calculated?

The slope of a tangent is calculated using the derivative of the curve at a specific point. This can be done using the limit definition of the derivative or by using the rules of differentiation.

What is the significance of finding slope of a tangent?

Finding the slope of a tangent is important in many fields of science, especially in physics and engineering. It allows us to determine the velocity, acceleration, and other important properties of a moving object at a specific point on its trajectory.

Can the slope of a tangent be negative?

Yes, the slope of a tangent can be negative. This indicates that the curve is decreasing at that point, and the tangent line is sloping downwards from left to right.

What is the relationship between slope of a tangent and the slope of a secant?

The slope of a tangent is the limit of the slope of a secant as the two points on the curve get closer and closer together. In other words, the slope of a secant is the average rate of change between two points, while the slope of a tangent is the instantaneous rate of change at a single point.

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