Line curve

[Myth]

What is the y-intercept of the tangent line to the curve y=e^x-4 @ the point (5,e)?

Can someone help me

 

[lev888]

What do you need to know to find the y-intercept?

 

[topsquark]

What is the y-intercept of the tangent line to the curve y=e^x-4 @ the point (5,e)?

Can someone help me

You need to use parenthesis:
y = e^x-4: $$y = e^x - 4$$y = e^(x - 4) : $$y = e^{x - 4}$$
What is the slope of the tangent line at x = 5?

-Dan

 

[Myth]

You need to use parenthesis:
y = e^x-4: $$y = e^x - 4$$y = e^(x - 4) : $$y = e^{x - 4}$$
What is the slope of the tangent line at x = 5?

-Dan

Oh sorry . That was supposed to be y = e^(x - 4)

 

[Myth]

What do you need to know to find the y-intercept?

Is this right?

 

[Myth]

Oh sorry . That was supposed to be y = e^(x - 4)

 

[Harry_the_cat]

You have found y' correctly.
At (5, e), m = e^(5-4) = e (you haven't evaluated m at the point given.)

Now find your equation of the tangent.

BTW in the box, you can't just swap the order around. ie a-b is not the same as b-a.
Come back with your final answer.

 

[HallsofIvy]

Surely you know that the "intercept" of a line is NOT a function of x?!

Apparently, you forgot that x was equal to 5.

 

[Myth]

Surely you know that the "intercept" of a line is NOT a function of x?!

Apparently, you forgot that x was equal to 5.

Right?

 

[MarkFL]

Yes, the family of lines through the given point is:

[MATH]y=m(x-5)+e=mx+e-5m[/MATH]
And we know:

[MATH]m=\left.\frac{df}{dx}\right|_{x=5}=e[/MATH]
Hence, the $y$-intercept is:

[MATH]e-5(e)=-4e\quad\checkmark[/MATH]

 

[HallsofIvy]

Yes, though I would have been inclined to write it as y= e(x- 4) but that difference is not important.

 

[Myth]

Yes, the family of lines through the given point is:

[MATH]y=m(x-5)+e=mx+e-5m[/MATH]
And we know:

[MATH]m=\left.\frac{df}{dx}\right|_{x=5}=e[/MATH]
Hence, the $y$-intercept is:

[MATH]e-5(e)=-4e\quad\checkmark[/MATH]

Oh . Thank you very much