Calculating the equations for the tangent/normal lines

[fulton33]

Homework Statement

Use the table to write the equation for tangent lines at given values of x.

Relevant Equations

y-y0=m(x-x0)

9. When I do this problem I know my slope is -3 because f'(2)=-3. I then went and substituted and got
y+5=-3(x-2) which simplified to y=-3x+1

10. I get lost here because the tangent slope would be 0, which would give me the equation y=-2. The normal means perpendicular and the perpendicular slope to 0 is undefined. Not sure if that is right and what to do after.

11. I did the same steps in 9. The slope is 3 and I get the equation y-4=3(x+1) which simplifies to y=3x+7

12. I am lost here as well. The tangent slope would be DNE, which would mean the normal slope to be 0. When I plug 0 in for m and (2,0) for x and y I get y=0. I think that is wrong.

 

[Mark44]

10. I get lost here because the tangent slope would be 0, which would give me the equation y=-2. The normal means perpendicular and the perpendicular slope to 0 is undefined. Not sure if that is right and what to do after.

If the slope of the tangent line is 0, its normal will be a vertical line of the form x = k, where k is the x-value at the point of tangency.

12. I am lost here as well. The tangent slope would be DNE, which would mean the normal slope to be 0. When I plug 0 in for m and (2,0) for x and y I get y=0. I think that is wrong.

This is the converse of #10. If the tangent slope is undefined, a line perpendicular to it will have slope 0.

 

[fulton33]

If the slope of the tangent line is 0, its normal will be a vertical line of the form x = k, where k is the x-value at the point of tangency.
This is the converse of #10. If the tangent slope is undefined, a line perpendicular to it will have slope 0.

10. Does that mean for number 10 the equation would be x=0 because at x=-1 f'(-1)=0?

12. Does that mean that for number 12 y=0 would then be correct?

 

[Mark44]

Does that mean for number 10 the equation would be x=0 because at x=-1 f'(-1)=0?

No. You're given information about the point (-1, -2).

Does that mean that for number 12 y=0 would then be correct?

Yes.

 

[fulton33]

No. You're given information about the point (-1, -2).
Yes.

That makes sense about 10. That would make it x=-1?

 

[Mark44]

Yes, that's better.