Line curve

M

Myth

New member
Joined
Apr 3, 2020
Messages
8
What is the y-intercept of the tangent line to the curve y=e^x-4 @ the point (5,e)?

Can someone help me
 
Myth said:
What is the y-intercept of the tangent line to the curve y=e^x-4 @ the point (5,e)?

Can someone help me
Click to expand...
You need to use parenthesis:
y = e^x-4: [math]y = e^x - 4[/math]y = e^(x - 4) : [math]y = e^{x - 4}[/math]
What is the slope of the tangent line at x = 5?

-Dan
 
topsquark said:
You need to use parenthesis:
y = e^x-4: [math]y = e^x - 4[/math]y = e^(x - 4) : [math]y = e^{x - 4}[/math]
What is the slope of the tangent line at x = 5?

-Dan
Click to expand...

Oh sorry . That was supposed to be y = e^(x - 4)
 
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.
 
Surely you know that the "intercept" of a line is NOT a function of x?!

Apparently, you forgot that x was equal to 5.
 
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]
 
Yes, though I would have been inclined to write it as y= e(x- 4) but that difference is not important.
 
MarkFL said:
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]
Click to expand...
Oh . Thank you very much ❣️
 
You must log in or register to reply here.
Top