Problem with equation of line tangent to curve

In summary, the equation of the tangent line to the curve at the point (25, f(25)) is y=7/10x + 41/2, or y-y_1=7/10(x-x_1), where y_1=38 and x_1=25.
  • #1
Chas3down
60
0

Homework Statement


Now use your answer from part (a)(This anwser is f'(25) = 7/10, which is correct) to find the equation of the tangent line to the curve at the point (25, f(25)).


Homework Equations


f(x) = 7*sqrt(x)+3



The Attempt at a Solution


f'(25) = 7/10
f(25) = 38
y=mx+b
38=7/10*25+b

y=7/10x + 41/2

This should be the correct answer... but it won't accept it.


if you want to view the entire problem, http://i.imgur.com/xtVehti.png
 
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  • #2
Try using something other than y=mx+b. Do you know any other ways to write the equation that doesn't rely on B?
 
  • #3
Yosty22 said:
Try using something other than y=mx+b. Do you know any other ways to write the equation that doesn't rely on B?

we are given y= ?

so y=mx+b is really the only linear function they could be looking for.
 
  • #4
Try y-y_1=m(x-x_1). You are given y_1 and x_1 (or can easily find them) and you have already solved for m. The rest is plugging in and simplifying.
 
  • #5
Yosty22 said:
Try y-y_1=m(x-x_1). You are given y_1 and x_1 (or can easily find them) and you have already solved for m. The rest is plugging in and simplifying.

edit: i am an idiot... had a - instead of a +
 

What is the equation of the line tangent to a curve at a given point?

The equation of a line tangent to a curve at a given point can be found by taking the derivative of the curve at that point and using the point-slope form of a line.

How do you find the slope of a tangent line to a curve?

The slope of a tangent line to a curve can be found by taking the derivative of the curve at the given point. This derivative represents the rate of change of the curve at that point, which is equal to the slope of the tangent line.

Why is it important to find the equation of the tangent line to a curve?

The equation of the tangent line to a curve is important because it allows us to approximate the behavior of the curve at a specific point. It also helps us to find the maximum and minimum points on a curve, which can have practical applications in fields such as economics and engineering.

Is it possible for a curve to have more than one tangent line at a given point?

No, a curve can only have one tangent line at a given point. This is because the tangent line represents the instantaneous rate of change of the curve at that point, and there can only be one unique rate of change at a specific point.

Can the equation of a tangent line be used to find the point of intersection between two curves?

Yes, the equation of a tangent line can be used to find the point of intersection between two curves. This can be done by setting the two equations equal to each other and solving for the x-coordinate of the point of intersection.

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