Differentiation (1 Viewer)

[WEMG]

Hi,
Can someone give me an example for finding angles of inclination of the tangent and normal and help me do this question:

Find the equation of the tangent and normal to the graph of
f(x) = x^2 - 8x + 15 at the (4, -1).

 

[hscishard]

Tangents and normals always make 90

 

[fullonoob]

normal should be all real x, i think, or x = 4, someone clarify please

Normally to find angle of inclination you use the formula tan @ = |m1-m2/ 1+m1m2| for acute angles

 

[ohexploitable]

Tangents and normals always make 90

I think he/she means with the x-axis.

 

[hscishard]

Ohh I see what you're asking
The question.
Differentiate. Sub 4 to find gradient at that point. You'll find it is 0. This is a stationary point.
Use gradient point to find tangent.
y+1 = 0(x-4)
y=-1
Thats the tangent.
It would be common sense that the normal would be x =4. Sketch it.

 

[WEMG]

thanks!!!

 

[fullonoob]

the reason for horizontal tangent at (4,-1) is because thats the parabola's vertex.
If it didnt specify the point (4,-1) then normal could be all real x i believe (for normal to y = -1).
But in this case its x = 4

 

[mirakon]

Basic Procedure:

Finding tangent and normal at Point P

1. Differentiate f(x). Let derivative be f'(x)
2. Sub x-value of point P for where you want tangent into f'(x). Let the result be m.
3. m is thus the gradient of the tangent at that point. To find equation of tangent use

y-y1=m(x-x1) where x1 and y1 are the x and y coordinates of P.

4. For normal, gradient is -1/m. Sub this into the general equation formula as in step 3.