Mmm.... one more thing? (1 Viewer)

[epicFAILx]

Uh, Tangents and Normals. Im not to sure about.

Like eg: a simple y=x^2 (finding the gradient of the tangent at x=2)
do you derive it first then substitute for x


When i think of tangents and normals i just have a blank look on my face O_______O

 

[slyhunter]

Find then sub in your x coordinate into it to get your tangent gradient.

to get your normal gradient, where m is your tangent gradient.

Use to find your equations.

 

[brettymaccc]

Uh, Tangents and Normals. Im not to sure about.

Like eg: a simple y=x^2 (finding the gradient of the tangent at x=2)
do you derive it first then substitute for x


When i think of tangents and normals i just have a blank look on my face O_______O

To find equation of tangent at a point;
1. Derive the equation of the curve. This finds a general expression for the gradient of the curve. (ie. this case, dy/dx = 2x).
2. Substitute in the specific x-value you want, this will tell you the gradient of the curve at that point, ie. the gradient of the tangent at that point. (in this case, dy/dx = 4 at x = 2)
3. Find the corresponding y-value of the curve at the point (ie. at x = 2, y = 4).
4. Use point-gradient formula, with your gradient as 4, and your point as (2,4).

To find equation of normal, it is exactly the same, however you merely take the negative reciprocal of the found gradient - whether you do it before or after you sub in your x-value is irrelavent. (ie. if dy/dx = 4, then the gradient of your normal is -1/4); then use point gradient formula as before.