Calculus: Determine the constants from function
posted by mia .
The function h(x) = x^3 + bx^2 + d has a critical point at (2, 4). Determine the constants b and d and find the equation of h(x).
IM SO CONFUSED :(

dh/dx = 0 at critical points
dh/dx = 3 x^2 + 2 b x = 0
x (3x+2b) = 0
so
at (2,4), 3x+2b = 0 = 6 + 2b
so b = 3
so
h = x^3 3 x^2 + d
at x = 2, h = 4
4 = 8  12 + d
d = 0
so
h = x^3 3 x^2
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