Chapter 4
What is the derivative of f(x)=3x1/5+3x
3/5x-4/5+3
Evaluate each integral.
Math 9, boundaries (2 to -1) 6x(x2-1)2dx
27
Find the volume of the solid whose base is bounded by the circle x2+y2=9 with the indicated cross sections taken perpendicular to the x axis. Squares.
144
Find the critical points of the given function.
f(x)=x3-2x2+x
x= 1/3, 1
Evaluate each integral.
Math 9, boundaries (0, -1) 8x/(4x2+1)2dx
-.8
Find the area bound by the curves f(x)=x2-1 and f(x)=7-x2
21.33333
Find the intervals on which the function is increasing/ decreasing. Then identify the function's local minima/ maxima.
f(x)=-x3+2x2
x=0 min
x=4/3 max
Determine the position function if the velocity is v(t)=-32t+10 and the initial position is s(0)=2.
s(t)=-16t2+10t+2
Find the volume of the solid whose base is bounded by the functions y=x2 and y=6 with the indicated cross sections taken perpendicular to the y- axis. semi circle.
about 28.27
Find the intervals on which the function is concave up/ down. Then identify the function's local point(s) of inflection.
f(x)=x3-3x+3
x=0 point of inflection
(-Infinity,0) concave down
(0, infinity) concave up
Determine the position function if the velocity is v(t)=-32t+1 and the initial position is s(0)=2.
-16t2+t+2
Find the volume of the solid obtained by rotating the region enclosed by the graphs about the given line. y=x2, y=12-x, x=0, about the x- axis.
about 893.47
Find the intervals on which the function is concave up/down. Then identify the function's point(s) of inflection.
f(x)=-2x3+6x2-3
x=1 point of inflection
(-Infinity,1) concave up
(1, infinity) concave down
A city consumes at the rate of r(t)=100+72t-3t2 (in thousands of gallons per hour), where t is the number of hours past midnight. How much water is consumed between 10 am and 8 pm?
4800 gallons/ hour
Estimate the area under the curve y=x2 on the interval [0,2] using 6 rectangles and the left- endpoint evaluation method.
55/27