Equation of the tangent line to the curve

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Homework Help Overview

The problem involves finding the equation of the tangent line to the curve defined by the function 7*x*e^(x)+8 at the point (0,8). The subject area pertains to calculus, specifically the concepts of derivatives and tangent lines.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to calculate the derivative of the function to find the slope of the tangent line. There are attempts to apply the point-slope form of the line equation, with some questioning the correctness of the initial derivative calculation and the use of variables in the line equation.

Discussion Status

There is ongoing clarification regarding the correct application of the derivative and the point-slope form. Some participants suggest specific values for the slope and the final equation, while others express uncertainty about the initial attempts and the proper form of the equation.

Contextual Notes

Participants are navigating through the requirements of using point-slope form versus slope-intercept form, and there is mention of the need to evaluate the derivative at a specific point to find the slope.

kdpointer
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Homework Statement



Find an equation of the tangent line to the curve: 7*x*e^(x)+8 at (0,8)

Homework Equations



Derivative I guess?

The Attempt at a Solution



I know you have to take the derivative of the equation given which I think is

7*x*e^(x) + 7*e^(x)

Then you plug it into slope intercept form: y-y=m(x-x)

I did this and got y-8=(7*e^(x)*(x+1))*x, but apparently that's not right...

What did I do wrong? Maybe i just typed it in wrong?
 
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Calculate the slope first by plugging in x=0 into the derivative equation... then when you have the number for the slope, plug it into the slope intercept form.

The slope should just be a number.
 
Yeah, it's pretty wrong. In the line equation m is a constant. Otherwise, it wouldn't be a line, now would it? Put (0,8) into the derivative before you plug it into the line equation.
 
so essentially you have to use your x-intercept twice
 
So the slope is just 7?
 
Thus the final equation is y-8 = 7x ?
 
kdpointer said:
Thus the final equation is y-8 = 7x ?
it should probably be in slope-intercept form

y=mx+b
 
It says that point-slope form is fine.. but it would be y=7x+8
 
kdpointer said:
It says that point-slope form is fine.. but it would be y=7x+8

Yup. That's right.
 
  • #10
Alright.. thanks a lot!
 

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