Tangent/Normal with derivative

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In summary, a tangent line is a line that touches a curve at only one point and is parallel to the curve at that point. The slope of a tangent line is equal to the derivative at that point. The equation for a tangent line can be found using the point-slope form. A normal line is a line that is perpendicular to the tangent line at a given point on a curve and represents the direction of the curve's fastest change. The slope of a normal line is equal to the negative reciprocal of the slope of the tangent line.
  • #1
iRaid
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Homework Statement


Find the lines that are (a) tangent and (b) normal to the curve y=x3 at the point (1,1).

Homework Equations


The Attempt at a Solution


So first I found the derivative, 3x2. Then I used x=1 to find the slope which is 3.

(a)y-1=3(x-1)
y=3x-2

(b)y-1=(-1/3)(x-1)
y=(-1/3)x+(4/3)Not really sure if I found the slope correctly tho..
 
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  • #2
It looks good to me.

If two lines are perpendicular, then the product of their slopes is -1 .
 
  • #3
Looks good to me. I see no problem with a or b.
 
  • #4
Thanks :p
 

FAQ: Tangent/Normal with derivative

What is a tangent line?

A tangent line is a line that touches a curve at only one point, and is parallel to the curve at that point.

How is the slope of a tangent line related to the derivative?

The slope of a tangent line at a point on a curve is equal to the value of the derivative at that point.

What is the equation for a tangent line?

The equation for a tangent line can be found using the point-slope form: y - y0 = m(x - x0), where (x0, y0) is the point where the tangent line touches the curve, and m is the slope of the tangent line.

What does a normal line represent?

A normal line is a line that is perpendicular to the tangent line at a given point on a curve. It represents the direction in which the curve is changing most rapidly at that point.

How is the slope of a normal line related to the derivative?

The slope of a normal line is equal to the negative reciprocal of the slope of the tangent line at a given point on a curve. This means that if the slope of the tangent line is m, the slope of the normal line is -1/m.

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