Optimization in terms of CSlatt

1. To find optimization, you will first find the derivative of the equation. Next, set that derivative equal to 0 and solve for the variable.
2. Find the point on the line y=2x+3 that is closet to the origin. To optimize, you will first need to use the distance formula. d=sqr[(x)^2-(2x+3)^2]. Next, find the derivative of the new distance formula using a combination of the power rule and chain rule. (d^2)'=[2x+2(2x+3)*2] = (2x+8x+6)= 10x+12. Next set this equation equal to 0 and solve for x. 10x+12=0, 10x=-12, x=-6/5 and plug back into the original y= equation. y=2(-6/5)+3 = 3/5. The final answer comes to [(-6/5),(3/5)]
3. f'(x)=6x^2-10x-1
a) 2x^3-5x^2-x
b)2x^3-5x^2-x+69