# Thread: Tangency to a curve

1. ## Tangency to a curve

The equation of a line tangent to the curve y^2 - 2x - 4y =1 at (-2,1) is what?

The tangent line to the curve 3x^4 - 10x + 3 at x = 1 interets the x-axis at what point?

2. Originally Posted by syndicate
The equation of a line tangent to the curve y^2 - 2x - 4y =1 at (-2,1) is what?

The tangent line to the curve 3x^4 - 10x + 3 at x = 1 interets the x-axis at what point?
You must impicitly differentiate in te first problem, solve for $\displaystyle \frac{dy}{dx}$ and evaluate at the given pointto find the slope of the tangent line. Then, using the given point along with the slope, develope the equation for the line.

For the second, evaluate $\displaystyle \frac{dy}{dx}$ at $\displaystyle x=1$ to find the slope of the tangent line. then go back and plug 1 into the original function to have the necessary point needed to develop the equation to the tangent line. Then find the x-intercept of this line.

3. So for the first problem
dy/dx [2y-4] - 2 = 0
dy/dx = 2/2y-4 = 2/2(1) -4
dy/dx = 2/-2 = 1 = slope

y = mx + b
1 = (-1)(-2) + b
1 = 2 + b
-1 = b

y = -x -1 ?

Second problem:
12x^3 - 10 = dy/dx
dy/dx = 12(1)^3 - 10
dy/dx = 12 - 10 = 2 is the slope of the tangent line

3(1)^4 - 10 + 3
3 - 10 + 3 = -10 = y

y = mx + b
-10 = 2(1) + b
b = -12

y = 2x -12 is the slope of the tangent line?