1. FLORIN GJERGJAJ • INDIVIDUAL PROJECT: GUIDE FOR SOLVING 2008 FRQ #6

2. 2008 #6

3. Breaking down the question - They are asking for line tangent so you know that you will have to use the point slope formula = - The question gives us the derivative and the original function. So its time to see everything we have and what we need to figure out in order to plug it into the line formula. We know that . The function is . The derivative of the function is We are trying to find what m,y1, and x1 are at .

4. Solution to Part A -Derivative formula -- Function - Plug - Solve for y1 = -- Solve

5. ` What are they asking for? - They are asking for the x-coordinate of the point where f`(x) changes sign. - They are also asking to check if that point is a Relative Minimum ( - +), Relative Maximum (+  -) , or neither. Solution Test for Relative Extrema = 0 x= e The x-coordinate of the critical point of f is x= e and f`(x)=0 there.At x=e there is a relative maximum because f`(x) changes from positive to negative there

6. Breaking down the question -They are asking for the point of inflection so you know you have to find the second derivative function. Then you have to see where f``(x) changes sign. Solution-   Then you find when f``(x)= 0  -  Testing if sign changes which would make it a point of inflection There is a point of inflection at because f``(x) changes sign there

7. Part D is very simple . They simply want us to find the limit of f(x) as x approaches zero from the right. Solution  . Now to solve this we can use the L’Hopital rule. ==

8. Citations • http://www.math.uh.edu/~dgross/Web2006/M1313spring2010/reviewtest1fillpdf.pdf • http://apcentral.collegeboard.com/apc/public/repository/ap08_calculus_ab_q6.p • http://mszhao.com/ab.cfm • Mathtype • Snipping Tool • http://www.superbtutors.com/monterey/math-tutoring.htm