i can't seem to get the right answer?

Question

Find an equation of the tangent line to the curve at the point (49, 7).

y=sqrt(x)

Answer in the form y=

Answer 1

The equation of the tangent line is..
y = (1 / 14) * (x - 49) + 7
That can be simplified a bit.

Answer 2

Well, you need the slope first, so take the first derivative:
y = x^(1/2)
y' = (1/2)x^(-1/2)
= 1/(2√7)
Now, using the slope intercept form of a straight line:
y-y1 =m(x-x1) (Eq1)
y -49 = 1/(2√7)(x -7)
y = 1/(2√7)(x -7) -49
y = 1/(2√7)x -7(1/(2√7)) -49
=1/(2√7)x –(√7(1-14√7)/2)

Of course, if you want to approximate it you can just find the slope using a graphing calculator. Do it this way on a TI-82, TI-83 Plus, or TI-84.
a) Press Y=, enter your equation and press GRAPH.
b) Press 2nd, CALC, 6 to select dy/dx.
c) This should take you to the graphing screen. So, enter 7 and press ENTER. You’ll get dy/dx = .18898… That’s the slope, of course.

Then you can plug that and the point into Eq 1.
y-49= .18898(x-7) (Eq )
y = .18898x -.18898(7) -49
Then you can just plug those numbers into your calculator as arithmetic and get the answer. I’ll leave it to you to do the arithmetic.

Hope this helps.
FE

Answer 3

The slope of the line tangent to the curve at the given point
is equal to the first derivative of the given function (y = √x)
or y = x ** ½ evaluated for x at the desired point.
The first derivative (dy/dx) of y = x**½ is: dy/dx = 1/(2√x)
If x = 49, √x = 7, and 2√x = 14, so the slope is 1/14.
To find the y-intercept, we must go back to the y-axis on a
straight line from (49,7) with a slope of 1/14.
For every 14 units we go back, the line drops 1 unit, or for
every 7 units we go back, the line drops ½ unit. To get
back to the y-axis we go back left 49 units and at a slope
of 1/14, the line drops 3½ units, so it intersects the y-axis
at (0,3½). Thus the equation of the line in slope-intercept
form (y = mx + b) is y = x/14 + 3½
where m is the slope of the line and b is its y-intercept.
Simple, huh?

Answer 4

ok, sqrt(x) can be written as x^0.5

Now, take the derivative, giving you y' = 0.5x^(-0.5)

Plug in the x = 49 and get 0.5(1/7) = 1/14. The slope of the tangent line at that point is 1/14 or about 0.0714.

From here, you can find the equation, with the knowledge that the slope is 1/14.

So, our equation is y = x/14 + b

The y-intercept in this case is 49/14, so the final equation is
y = (x + 49)/14

Answer 5

your formula is the answer--just turn the ABBREVIATION into English words.

y=square root of x

since 7 is the square root of 49, you are done.