The slope of the tangent line to the parabola y = 3 x^2 + 4 x + 2 at the point ( 2 , 22 ) is: 2
The equation of this tangent line can be written in the form y = mx+b where m is:_______________?
and where b is:_______________?
- 8 years agoBest Answer
Agree with Iobo that m is the slope of the tangent line and b is the y-intercept of the tangent line. However, I would just add what the actual values are when applied to the parabola and its tangent you cited.
In this case, y' = 6x + 4 means that y'(2) = 16. So the the slope of the tangent line at x=2 is m=16.
To find b, the y-intercept of the tangent line, just use y=mx+b, your point (2,22) as (x,y), and m=16:
That gives 22 = 16(2) + b, or b = -10. Thus the equation of the tangent line to the parabola is y = 16x - 10.
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- Anonymous8 years ago
First, find the derivative:
Now, plug in x:
dy/dx=6(2)+4=16<------this is your slope (m)
Now plug this into the y=mx+b equation given your x,y coordinates to solve for b:
m is 16
b is -10
And your equation is y=16x-10
- frak1a12345Lv 68 years ago
y = mx + b is known as the "slope/intercept" form of a line equation.
m is the slope of the line and b is the y intercept of the line.
You plug in the 3 known quantities x, y and m (all are given to you) and solve for b.
- Wile E.Lv 78 years ago
y = 3x² + 4x + 2
dy/dx = 6x + 4
x = 2
y = 22
dy/dx = 6(2) + 4
dy/dx = 12 + 4
dy/dx = 16
b = y - [(dy/dx)(x)]
b = 22 - [16(2)
b = 22 - 32
b = - 10
Equation of Tangent Line:
y = 16x - 10
m = 16
b = - 10
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- loboLv 68 years ago
m is slope of the tangent line
b is the y intercept of the tangent line.