7) Solve for the given variable: 3r + 6 = 2r + 9
2 answers:
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For each curve, plug in the given point and check if the equality holds. For example:
(I) (2, 3) does lie on since 2^2 + 2*3 - 3^2 = 4 + 6 - 9 = 1.
For part (a), compute the derivative , and evaluate it for the given point
. This is the slope of the tangent line at the point. For example:
(I) The derivative is
so the slope of the tangent at (2, 3) is
and its equation is then
For part (b), recall that normal lines are perpendicular to tangent lines, so their slopes are negative reciprocals of the slopes of the tangents, . For example:
(I) The tangent has slope 7/4, so the normal has slope -4/7. Then the normal line has equation