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(Solved): The figure above shows the curve C with equation: = 23 + 32 11 6The curve cr ...
The figure above shows the curve C with equation:
???? = 2????3 + 3????2 ? 11???? ? 6
The curve crosses the ????-axis at the points ???? , ???? and ????(2,0). The tangent to ???? at ???? is the straight line ????1. The normal to ???? at ???? is the straight line ????2. The straight lines ????1 and ????2 meet at the point S.
3a) Find an equation of ????1. 3b) Show that ????????????? = 90°.
Expert Answer
To find the equation of line L1, which is the tangent to curve C at point R(2,0), we need to find the slope of the tangent at that point.Find the derivative of the equation of curve C with respect to x: Substitute x = 2 into the derivative to find the slope at point R: = 24 + 12 - 11 = 25Use the slope-intercept form of a line (y = mx + b) with the slope 25 and point R(2,0) to find the equation of line L1: y - 0 = 25(x - 2) y = 25x - 50Therefore, the equation of line L1 is y = 25x - 50.To show that angle ?PSR = 90°, we need to show that the slope of line L2, the normal to curve C at point P, is the negative reciprocal of the slope of line L1.