please help with the circle problem :[
I have some questions due tomorrow, and I'd really like to know if the answers are right.
1)
Find the intervals where f(x) is
a) concave up to positive infinity
b) concave up negative infinity to
c) Find all inflection points (2/3, 3.852)
2) Write the equation(s) of the vertical tangent(s) to the curve
y=-1 and x=1
Also, I have NOOoOOO clue how to do this problem:
A square is inscribed in a circle as shown below (ignore the circle with the triangle). As the square expands, the circle expands to maintain the four points of intersection. The perimeter of the square is increasing at the rate of 12 in/second.
a) Write the circumference of the circle as a function of the side of the square:
C(s)=2pi(s/squareroot of 2)
b) Find the rate at which the circumference of the circle is increasing
c) At the instant when the area of the square is 16 square inches, find the rate at which the area enclosed between the square and the circle is increasing.
d) The radius of a circle is decreasing at a constant rate of .2cm/s. In terms of circumference, what is the rate of change of the area of the circle?
thank you!!