Beach - Sandy Andy

a) R(t) is the rate at which sand is being removed by cubic yards/hour, so if you take the integral, it would give you the amount of sands by cubic yards (which the question is asking for )
eq: fnInt (2+5sin((4 pi t)/25), x, 0, 6) = about 31.816, so at t = 6, 31.816 cubic yards of sand has been removed

b) asking for amount of sand, so integral is needed,
fnInt(S(t)), x , 0, 6) - fnInt (R(t)), x, 0, 6) + 2500

c) asking for the rate, so no need to integrate, just plug in t=4
so... S(4) - R(4) = -1.909,
so at t = 4, the amount of sand is decreasing by 1.909 cubic yards/hour

d) Asking for amount of sand, so the graph of S(t) - R(t) would give you the slope, when the slope changes from - to +, you'll have a min,
at t= 5.1179 you have a minimum, that is where slope changes from - to + on the graph of S(t) - R(t) (slope graph)

Mean Value Thm

1. Green line - secant, blue-tangent

slope of point c is equal to f(b)-f(a)/b-a

2.Discontinuity and not differentiable functions prevent the slope of the tanget line and secant line from being parrallel

f(x) vs f ' (x)

1. From the Interval (-2,0)U(0,2), f(x) is increasing, f ' (x) is the slope of f(x), and the in that interval, the points are positive, positive slope = increasing
From (-infinity, -2) U (2, infinity), f(x) is decreasing, because the slope is negative, points on f ' (x) graph are negative in that interval

2.At x= -2, f ' (x) changes from negative to positive, making it a local minimum.
at x = 2, f ' (x) changes from positive to negative, making it a local maximum

3. In the interval (-infinity, -1.5) U (0,1.5) , the slope of the f ' (x) graph is positive, f ''(x) > 0 is concave up
in the interval (-1.5 , 0) U (1.5 , infinity), the slope of f '(x) is decreasing, f ''(x) < 0 is concave down

Which Mindset am i?

1. I think i am most likely in the Growth Mind-Set group because..

• Take on challenges
• Move my way over obstacles and..
• see effort as a way to master

2.By taking this class, i knew before hand that it was going to be a challenge, also i've worked my way over my problems in this class, and the effort paid off.

3.Its interesting, because now i know that i could really become more intelligent if i tried.

4.It'll really get me to take on more challenges, and do the same thing i've done in this class, and see how much more intelligent i'll become.