Fall+Week+09

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Monday 10/12
No School - Columbus Day

Tuesday 10/13
Choice of activities today due to the PSAT testing scheduled for tomorrow. Junior students worked on some practice questions for the PSAT while the seniors worked on some tangent line problems, practicing problem solving and derivatives. Here are the problems.

1-4. Find f '(x) given f(x).

1. f(x) = (x² + 1)/x 2. f(x) = x ^ pi 3. f(x) = (pi) ^x 4. f(x) = 1/ (3x³)

5. Find all values of x where f"(x) is greater than or equal to 1 if f(x) = 4x³ + 6x² - 23x + 7.

6. find the equations of all lines passing through (0,0) that are tangent to f(x)= x² - 2x + 4.

7. Find the two lines passing through (5, 7) that are tangent to y = x² - 2x + 1.

8. If y = 3x² + k is tangent to y = 4x, find k.

9. Find all values of x where the tangent line to the graph of y = 6x^(1/3) is perpendicular to -4x - y = -1.

10. Find a function y = ax² + bx + c whose graph has an x intercept at 1, a y intercept at 4.5, and a tangent line with slope -1 at its y intercept.

11. Find the values of "a" and "b" if the tangent to y = ax² + bx at (1,5) has slope 8.

12. Calculator problem. Find all values of x where the tangent line to y = 2x³ + 3x² - 9 is perpendicular to the tangent to y = 4x² + 4x + 5. all answers must be correct to three decimal places.

Here are the solutions:

1987 AB 2 Let f(x) = (1 - sinx) ^ 1/2 a) What is the domain of f? b) Find f '(x). c) What is the domain of f ' ? d) Write an equation for the line tangent to the graph of f at x = 0.

1990 BC 1 A particle starts at time t = 0 and moves along the x axis so that its position at any time t greater than or equal to zero is given by x(t) = ( t - 1)³(2t - 3). a) Find the velocity of the particle at any time. b) For what values of t is the velocity of the particle less than zero? c) Find the value of t when the particle is moving anfd the acceleration is zero.

**Thursday 10/15**
Today, we determined the derivatives of the inverse trigonometric functions:

Sin Cos:



Tan:

Sec:



All: Problems: