This is a true statement right?

[Saladsamurai]

If $$f(x)=x^3-6x+c_2$$ and I know that $$y=5-3x$$ is tangent at the point where x=1,
then I can say that at x=1 $$f(x)=x^3-6x+c_2|_{x=1}=5-3x.$$
Right? and then I can solve for $$c_2$$

I am getting the correct answer to my text problem, but I want to be sure that it is because my reasoning is correct.

Casey

 

[HallsofIvy]

I presume that by "$$f(x)=x^3-6x+c_2|_{x=1}$$", you mean f(1).
Your reasoning is correct but I would write f(1)= 1₃- 6(1)+ c²= 5- 3(1).

 

[Saladsamurai]

I presume that by "$$f(x)=x^3-6x+c_2|_{x=1}$$", you mean f(1).
Your reasoning is correct but I would write f(1)= 1₃- 6(1)+ c²= 5- 3(1).

I guess that is a shorter hand way of writing it. But I guess I wanted to be sure that it was indeed f(x)=y at x=1. That the function and the equation were equivalent.

Thanks,
Casey