Equation of Tangent Line

[Jason76]

What is the equation of the tangent line of:

\(\displaystyle 2x^{2} + 4x + 2\) passing thru x value \(\displaystyle 7\)

\(\displaystyle f'(x) = 4x + 4\)

\(\displaystyle 4x + 4 = 0\)

\(\displaystyle x = -4\)

Point it passes thru \(\displaystyle (x, f(7))\):

\(\displaystyle f(7) = 2(7)^{2} + 4(7) + 2 = 128\)

Point is \(\displaystyle (7, 128)\)

 

[pka]

What is the equation of the tangent line of:

\(\displaystyle f(x)=2x^{2} + 4x + 2\) passing thru x value \(\displaystyle 7\)

\(\displaystyle f'(x) = 4x + 4\)

\(\displaystyle 4x + 4 = 0\) incorrect! has nothing to do with it!

The point is \(\displaystyle (7,f(7))\) the slope is \(\displaystyle f'(7)\).

 

[Jason76]

What is the equation of the tangent line of:

\(\displaystyle 2x^{2} + 4x + 2\) passing thru x value \(\displaystyle 7\)

\(\displaystyle f'(x) = 4x + 4\)

Slope is \(\displaystyle f'(7)\)

\(\displaystyle f'(7) = 4(7) + 4 = 32\)

Point it passes thru \(\displaystyle (x, f(7))\):

\(\displaystyle f(7) = 2(7)^{2} + 4(7) + 2 = 128\)

Point is \(\displaystyle (7, 128)\)

Is this right?

\(\displaystyle y - y_{1} = m(x - x_{1})\)

\(\displaystyle (y - 128) = 32(x - 7)\)

\(\displaystyle (y - 128) = 32x - 224\)

\(\displaystyle y = 32x - 96\) (equation of the tangent line at \(\displaystyle (7,128)\) Look right?

 

[srmichael]

What is the equation of the tangent line of:

\(\displaystyle 2x^{2} + 4x + 2\) passing thru x value \(\displaystyle 7\)

\(\displaystyle f'(x) = 4x + 4\)

Slope is \(\displaystyle f'(7)\)

\(\displaystyle f'(7) = 4(7) + 4 = 32\)

Point it passes thru \(\displaystyle (x, f(7))\):

\(\displaystyle f(7) = 2(7)^{2} + 4(7) + 2 = 128\)

Point is \(\displaystyle (7, 128)\)

Is this right?

\(\displaystyle y - y_{1} = m(x - x_{1})\)

\(\displaystyle (y - 128) = 32(x - 7)\)

\(\displaystyle (y - 128) = 32x - 224\)

\(\displaystyle y = 32x - 96\) (equation of the tangent line at \(\displaystyle (7,128)\) Look right?

Yes

 

[lookagain]

What is the equation of the tangent line of:

---->\(\displaystyle \ \ 2x^{2} + 4x + 2 \ \) <----

passing thru x value \(\displaystyle 7\)

\(\displaystyle f'(x) = 4x + 4\)

Jason76, you have posted that wrong twice, once in two different posts.

That line must be "\(\displaystyle f(x) = 2x^2 + 4x + 2, \ \)" so that the line below it with f'(x) follows and makes sense.