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danne89
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Consider the pababola y=x^2+bx+c. Find the values of b and c such that the line y=2x is tangent to the point (2,4).
I've no clue at all...
I've no clue at all...
You have y = 2x as the tangent line.. and you know that y' = 2x + b and thus you can substitute x = 2 into y' to get y' = 4 + b and from the question you know y' = 2... and so 2 = 4 + b; b = -2danne89 said:Consider the pababola y=x^2+bx+c. Find the values of b and c such that the line y=2x is tangent to the point (2,4).
I've no clue at all...
The concept involves finding the values of b and c in a quadratic equation by using the tangent line at a specific point on the curve.
The formula is b = y - (x^2 / 4c) and c = (y - bx) / x^2, where (x,y) is the point on the curve where the tangent line is drawn.
Finding the values of b and c allows for the construction of the quadratic equation, which can be used to model various real-world scenarios and make predictions.
The steps include finding the slope of the tangent line at the given point, substituting it into the formula, and then using the resulting equations to solve for b and c.
Yes, this method can be used for any point on the curve, as long as the slope of the tangent line at that point is known.