Calculating the equations for the tangent/normal lines

fulton33
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Homework Statement
Use the table to write the equation for tangent lines at given values of x.
Relevant Equations
y-y0=m(x-x0)
IMG_3607.jpeg

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.
 
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fulton33 said:
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.
fulton33 said:
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.
 
Mark44 said:
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?
 
fulton33 said:
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).
fulton33 said:
Does that mean that for number 12 y=0 would then be correct?
Yes.
 
Mark44 said:
No. You're given information about the point (-1, -2).
Yes.
That makes sense about 10. That would make it x=-1?
 
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