Expert: Paul Klarreich - 1/1/2010

Question
QUESTION: I saw another question about this but the one i have seems different enough in my opinion. my question is asking me :

The slope of the tangent line to the curve y = 4/x at the point ( 7 , 0.5714 ) is:
The equation of this tangent line can be written in the form y = mx+b where m is:
and where b is:

I dont even know where to start, let alone how to do it

ANSWER: Questioner: Kevin
Country: United States
Category: Calculus
Private: No
Subject: Slope Of tangent.
Question: I saw another question about this but the one i have seems different enough in my opinion. my question is asking me :

The slope of the tangent line to the curve y = 4/x at the point ( 7 , 0.5714 ) is:
The equation of this tangent line can be written in the form y = mx+b where m is:
and where b is:

I dont even know where to start, let alone how to do it
.................................................
This really is just like the others:

1. The slope of the tangent line to the curve y = 4/x at the point ( 7, 4/7 ) is just the derivative at  x = 7.

2. Once you have that, you have your m, and use the point-slope form:

y - y0 = m(x - x0)

with x0 = 7,  y0 = 4/7

Do a little algebra and you can get it in the form y = mx + b.


---------- FOLLOW-UP ----------

QUESTION: i have another like this, but there is no second value iven, that i recognize at least it says:

Suppose that f(x) = 7 x^2 + 2 x.

(A) Find the slope of the line tangent to f(x) at x=3.

(B) Find the instantaneous rate of change of f(x) at x=3.

(C) Find the equation of the line tangent to f(x) at x=3. y=

Answer
Questioner: Kevin
Country: United States
Category: Calculus
Private: No
Subject: Tangent line
Question: QUESTION: I saw another question about this but the one i have seems different enough in my opinion. my question is asking me :

The slope of the tangent line to the curve y = 4/x at the point ( 7 , 0.5714 ) is:
The equation of this tangent line can be written in the form y = mx+b where m is:
and where b is:

I dont even know where to start, let alone how to do it

ANSWER: Questioner: Kevin
Country: United States
Category: Calculus
Private: No
Subject: Slope Of tangent.
Question: I saw another question about this but the one i have seems different enough in my opinion. my question is asking me :

The slope of the tangent line to the curve y = 4/x at the point ( 7 , 0.5714 ) is:
The equation of this tangent line can be written in the form y = mx+b where m is:
and where b is:

I dont even know where to start, let alone how to do it
.................................................
This really is just like the others:

1. The slope of the tangent line to the curve y = 4/x at the point ( 7, 4/7 ) is just the derivative at  x = 7.

2. Once you have that, you have your m, and use the point-slope form:

y - y0 = m(x - x0)

with x0 = 7,  y0 = 4/7

Do a little algebra and you can get it in the form y = mx + b.


---------- FOLLOW-UP ----------

QUESTION: i have another like this, but there is no second value given, that I recognize at least it says:

Suppose that f(x) = 7 x^2 + 2 x.
..........................................
This is REALLY REALLY just like the others.


(A) Find the slope of the line tangent to f(x) at x=3.

1. You mean "the line tangent to THE GRAPH OF y = f(x)"

2. That is just the derivative at  x = 3.

(B) Find the instantaneous rate of change of f(x) at x=3.

That is just the derivative at  x = 3.  (did I say that before?)


(C) Find the equation of the line tangent to f(x) at x=3. y=

You mean "the line tangent to THE GRAPH OF y = f(x) at  x = 3"

Once you have f'(3), you have your m, then use the point-slope form:

y - y0 = m(x - x0)

with x0 = 3,  y0 = f(x0) = f(3)

and you are on your way.