AP CALC AB :: WORKED OUT PROBLEMS :: PROBLEMS XII:: Please refer to the images below for a step-by-step work out of problems. We will go over it during next lunch tutoring session ::
1) The radius of a circle is decreasing at a constant rate of 0.1 cm per second. In terms of circumference C, what is the rate of change of the area of the circle, in square cm per second?
2) In the xy-plane, the graph of a twice differentiable function y = f(x) is concave up on the open interval (0,2) and is tangent to the line y = 3x - 2 at x=1. Which of the following statements must be true about the derivative of f? (Choose one)
A) f'(x) > 0 on interval (0.9, 1.1)
B) f'(x) is > or = to 3 on interval (0.9,1)
C) f'(x) is constant on interval (0.9,1.1)
3) The number of people who've entered a museum on a certain day is modeled by the function f(t) where t is measured in hours since the museum opened that day. The number of people who've left the museum since it opened that same day is modeled by a function g(t). if f'(t) = 380(1.02^t) and g'(t)=240+240sin(pi(t-4)/12), at what time t, for 1<t<11 is the number of people in in the museum at a maximum?
1) The radius of a circle is decreasing at a constant rate of 0.1 cm per second. In terms of circumference C, what is the rate of change of the area of the circle, in square cm per second?
2) In the xy-plane, the graph of a twice differentiable function y = f(x) is concave up on the open interval (0,2) and is tangent to the line y = 3x - 2 at x=1. Which of the following statements must be true about the derivative of f? (Choose one)
A) f'(x) > 0 on interval (0.9, 1.1)
B) f'(x) is > or = to 3 on interval (0.9,1)
C) f'(x) is constant on interval (0.9,1.1)
3) The number of people who've entered a museum on a certain day is modeled by the function f(t) where t is measured in hours since the museum opened that day. The number of people who've left the museum since it opened that same day is modeled by a function g(t). if f'(t) = 380(1.02^t) and g'(t)=240+240sin(pi(t-4)/12), at what time t, for 1<t<11 is the number of people in in the museum at a maximum?
