It is given that an equation of the tangent line to the graph of y=g(x) at x=9 is 6x+9y=-27.?
It follows that y=? is the equation of the tangent line to y=g(x^2) at x=3
and that y=? is the equation of the tangent line to y=(g(x))^2 at x=9.
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answers:
khalil say: the m of the line
9y = -27 -6x
y = (-2/3)x - 3
m = -2/3
g(x) = ax² + bx + c
g'(x) = 2ax + b
g'(9) = 18a + b = -2/3◄
x = 9 → y = (-2/3) (9) - 3 = -9
-9 = a(9)² + b(9) + c
-9 = 81a + 9b +c◄
two equations and three unknowns
assume c = 0
18a + b = -2/3
-9 = 81a + 9b
a = 1/27 and b = -4/3
g(x) = (1/27) x² - (4/3) x
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