calculus
posted by samantha on .
determine the point of intersection of the tangents at the points of inflection to the curve f(x)= x^4 – 24x^2 – 2

y' = 4x^3  48x
y '' = 12x^2  48
at points of inflection, y'' = 0
12x^2 = 48
x^2 = 4
x = ±2
when x=2 , f(2) = 16  96  2 = 82 , slope = 32  96 = 64
when x = 2, f(2) = 82 , slope = 32 + 96 = 64
1st tangent: slope = 64, point is (2,82)
82 = 64(2) + b
b=46
first tangent equation: y = 64x + 46
2nd tangent: slope = 64 , point is (2,82)
82 = 64(2) + b
b = 46
second tangent is y = 64x + 46
intersection of y = 64x + 46 and y = 64x + 46
64x + 46 = 64x + 46
128x = 0
x = 0, then y = 46
the two tangents intersect at (0,46)