Need to find the y -intercept of the tangent to y = 18 x

dresu9dnjn 2022-05-07 Answered
Need to find the y-intercept of the tangent to y = 18 x 2 + 2 at point ( 1 , 6 ).
I keep getting 0, but I don't think that's right.
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Answers (2)

Corinne Choi
Answered 2022-05-08 Author has 10 answers
Step 1: Compute the tangent line.
- The tangent line is a line passing through the point ( 1 , 6 ) with the same slope as the curve that that point.
- In order to write down a line, you need a point on the line and the slope of the line. You already have a point, but you need to find the slope of the line.
- The slope of the line is the derivative at the point ( 1 , 6 ), since the function is
18 x 2 + 2 ,
its derivative is
36 x ( x 2 + 2 ) 2
plugging in x = 1 from the point ( 1 , 6 ), we get that the slope is
36 3 2 = 4.
This is the slope of the line of interest.
- Therefore, using the point-slope form of a line, you get that the tangent line is y 6 = ( 4 ) ( x 1 ).
Step 2: Find the y-intercept.
- You have the point-slope form of a line, to get y 6 = 4 ( x 1 ). We can turn this into slope-intercept form to get y = 4 x + 10.
- Therefore, your y-intercept is 10.
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studovnaem4z6
Answered 2022-05-09 Author has 3 answers
First you find the slope of tangent line at the point of tangency. Slope of tangent line is derivative of the function evaluated at the point of tangency. For y = 18 / ( x 2 + 2 ) we use quotient rule to get y = 36 x / ( x 2 + 2 ) 2 . m = y ( 1 ) = 4 is the slope and y = 6 4 ( x 1 ) is the equation of the tangent line. To find the y intercept we let x = 0 and get y = 10. Thus the point ( 0 , 10 ) is the y intercept of the tangent line.
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