Presentation on theme: "4. The derivative of f is x2(x - 2)(x + 3) . At how many points will"— Presentation transcript:
1 4. The derivative of f is x2(x - 2)(x + 3) . At how many points will 1. If f(x) = , then f ‘ (x) =2.Advanced Placement Calculus Semester One Review Name:___________________Calculator Active Multiple ChoiceIf x3 + 3xy + 2y3 = 17, then4. The derivative of f is x2(x - 2)(x + 3) . At how many points willthe graph of f have a relative maximum?
2 5. If f (x) = sec x + csc x, then f ‘(x) = 6. Find the x-coordinates of all points of inflection for the functionLetThe circumference of a circle is increasing at a constant rate of 5 feet per second.Find the rate at which the radius is increasing.8.
3 Advanced Placement Calculus Semester One Review Advanced Placement Calculus Semester One Review Name:___________________Calculator Free ResponseSuppose the distance in feet covered by a car moving along a straight road t secondsafter starting from rest is given by the function f (t) = 3.12t2 sin(0.3t)a. Find the average velocity of the car over the interval for t = 13 to t = 33 seconds.b. Find the time t in the interval t = 13 to t = 33 where the velocity of the car is equalto the average velocity.c. Find the instantaneous velocity when t = 33 secondsd. Find the acceleration of the car when t = 33 seconds.
4 Let A(x) be the area of the rectangle bounded by the x- and y- axis and the curve as shown below.A. Find the dimension of this rectangle such that its area is a maximum.B. Verify that when the area is a maximum the length of the rectangle is the same asx-coordinate of the point of inflection of the graph of y.yxc
5 3. If f (x)=cos2x, then f ´´ ()= Advanced Placement Calculus Semester One Review Name:___________________No Calculator Multiple Choice1. If , then f ‘ (8)=2.3. If f (x)=cos2x, then f ´´ ()=4. If is both continuous and differentiable, then a =Find the limit(a) (b) (c) (d) (e) This limit does not exist.
6 7. What is the slope of the tangent line to the curve at the point where x = 2?8. For what value of x does the function havea relative minimum?6. In the given interval 0 < x < 2, the function has critical numbers at9. The equation of the line tangent to at the point (1,5) is
7 Advanced Placement Calculus Semester One Review Advanced Placement Calculus Semester One Review Name:___________________No Calculator Free ResponseGraph of y = f´(x)The graph of the derivative of f (x) or f ’ (x) is shown. f ’ (x) has horizontal tangentsat the points x = -5, -2, and 2.a. Find the x-coordinate(s) of any relative extrema of f (x) and classify each asmaximum or minimum. Justify your answer(s).b. Find the interval(s) where f (x) is concave down.Justify your answer(s)c. Find the x-coordinate of the absolute maximum of f (x).
8 A circle is inscribed in a square as shown to the right. The circumference of the circle is increasing at aconstant rate of 5 feet per second. As the circle expand,the square expands to maintain the condition oftangency. (Hint: A circle with a radius of r had acircumference of C=2r and an area of A = r 2)A. Find the rate at which the perimeter of the square isincreasing. Be sure to indicate units of measure.B. At the instant when the area of the circle is 25 in2,find the rate of increase in the area enclosed betweenthe square and the circle.