Question

Calc Optimization Help Please, What am I doing wrong?

Answer 1

Calc Optimization Help Please?
Find the point on the parabola 2y = x^2 that is closest to the point (-4,1).

so d^2 = (x^2 + 4 ) ^2 + [(x^2 -2)/2]^2
then I differentiate both sides

2dd' = 2(2x)(x^2+4) + 2(2x)[(x^2-2)/2]
d' = 0 right?

so 0=4x^3 + 16x + x^3 - 2x

5x^3 + 14x = 0
/....



but the answer is x = -2? :(

Answer 2

your distance expression is off
distance between (-4,1) and (x,y(x)) is
\[\sqrt{(x+4)^{2} + (y(x) -1)^{2}}\]
where y(x) = x^2 / 2

Answer 3

what @dumbcow said, usually I try to draw it first so it gets easier for me to set the right unknowns/parameters