Advanced Placement Calculus AB Practice
Section II Part B
A graphing calculator is not allowed for the following problems.
1.Write an equation for the line tangent to the curve x2
+ 4x + y3
= 4 at the point (1, -1).
2. dy/dx = (x + 1)2
Sketch a slope field for the given differential equation at the points indicated.
3. dy/dx = (x + 1)2
Let y = f(x) be the solution of this equation with the initial condition f(1) = 1. What is the equation of the tangent to the graph of f at x = 1?
4. dy/dx = (x + 1)2
Find the solution y = f(x) to the given differential equation with the initial condition f(1) = 1.
5. Consider the closed curve in the xy plane given by 2x2
+ 5x + y3
+ y = 8.
Show that dy/dx = -(4x + 5)/(3y2
+ 8y + 1).
The graph of function f is shown above. Let:
Calculate g(3). Does g have a relative minimum or a relative maximum at x = -1? Calculate g"(0).
7. Let f be the function given by f(x) = (2x2
+ 5x -1)7
Write the equation for the line tangent to f(x) in x = 0.
8. Find the coordinates of the two points on the x2
- 2x + 4y2
+ 16y + 1 = 0 closed curve where the line tangent to the curve is vertical.
Verify your answers.