I was doing some homework and came across a couple of problems I was unsure of. The first set is FTC and the latter is motion along a line. These are quite a few problems and most of them are already solved. They don't have to be checked; I just need help on the blank ones.
Suppose h(x)= integral of f(t) [0,x], where f(t) is shown in the graph below.
The image is attached.
1. Find the critical points of h(x).
-At first, I had 5 and 11 because those are the points that f(t) =0. I changed the critical point to 0, though, because the integral with the bounds [0,0] would equal 0.
2. Identify the values of x when h(x) has a relative minimum and/or maximum.
-This is where I'm having the most trouble. I THOUGHT I had an idea of what to do, and found where the values of f(x) increased and decreased....yeah, I'm very confused on this problem.
3. Find the absolute minimum and maximum values of h(x) on [0,12].
-The absolute min I got was h(12)=-1 and the absolute max I got was h(0)=-4.
Motion along a line:
From its initial position of s(0)=-3, a particle moves along a linear path with a known velocity of v(t)=t^2-3t-4, where v(t) is measured in meters per second and t is greater than or equal to 0.
1. Find the time when the particle has an acceleration of 9 meters per squared second.
-I solved this and got s(6)=147
2. Find a function to represent the position of the particle at any time t.
-s(t)=s(0) + integral of u^2-3u-4 du [0,t]
3. Find the position of the particle when its velocity is zero.
-I was unsure so I just solved v(0)=-4.
4. Determine when the velocity of the particle is positive and when it is negative.
-This is the problem I had no clue on.
5. Find the distance traveled by the particle on the interval 0 less than/equal to t less than/equal to 5.
-I solved it and got 21.50.