Page 2.49 by xmung on June 12, 2005 at 12:01 am Chapter: The Great Leap ForwardLocation: Magellan Island

Let’s see.

g(x) = sqrt(x) * f(x)

g'(x) = 1/sqrt(x) * f(x) + f'(x) sqrt(x)

g'(4) = 1/sqrt(4) * f(4) + f'(x) sqrt(4)

g'(4) = 1/2 * 3 + 5 * 2

g'(4) = 0.75 + 10

g'(4) = 10.75

Way to go Fatima.

Oh wait, I goofed the square root rule and some of the simplifying. I think I got suckered by a confirmation bias.

sqrt(x) = x^(1/2)

d sqrt(x)/dx = (1/2) x^(-1/2) = 1/(2sqrt(x))

Therefore,

g'(x) = f(x)/(2sqrt(x)) + f(x) sqrt(x)

g'(4) = f(4)/(2sqrt(4)) + f(4) sqrt(4)

g'(4) = 3/(2*2) + 5 * 2

g'(4) = 3/4 + 10

g'(4) = 10.75

Y’know, I’ve always wondered about this page. If Fatima was confident she could solve the math problem, why were they so concerned about how Kaycee could breathe in the first place? She didn’t need to dive at all.

Help fight off any attacks against Fatima, maybe… mind you, I wouldn’t tagle with her in her element!