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afcwestwarrior
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y=1+2x-xcubed, (1,2)
You've got the slope in this formula. y=-x+3 is the same as saying y=-1x+3. And since y=mx+b, what do you suppose m is?afcwestwarrior said:the answer isy=-x+3, but i need to figure out the slope
When finding the equation of the tangent line to a curve, we are essentially determining the line that touches the curve at a specific point. This line represents the instantaneous rate of change, or slope, of the curve at that point.
To find the equation of the tangent line, we use the derivative of the curve at the given point. This derivative represents the slope of the tangent line. Then, we use the point-slope form of a line to plug in the slope and the given point to find the equation.
Yes, the tangent line can be found at any point on a curve. However, the equation of the tangent line will be different for each point on the curve.
You will need the x-coordinate of the point at which you want to find the tangent line, and the original equation of the curve. From there, you will use the derivative of the curve at the given point to find the slope of the tangent line.
Finding the equation of the tangent line allows us to understand the behavior of a curve at a specific point. It also helps us find the rate of change of the curve at that point, which is useful in many real-world applications such as physics and economics.