EXTRA CREDIT: +5 points



Ch 3 - Day 3 AP Calculus BC Name:

More Derivative and Tangent Line Problems

NO CALCULATOR!!!

1. The graph of the equation [pic] has a slope equal to 5 at exactly two points. Find the coordinates of the points.

2. Find the value of c , where the line l tangent to the graph of [pic]at ( 0 , 1 ) intersects the x-axis.

3. Find the equations of all lines through the origin tangent to the parabola [pic].

4. Find all ordered pairs ( x , y ) on [pic] and [pic] such the tangent lines to the curves are parallel.

5. Find the equations of the tangent lines to the graph of [pic] that pass through the point ( −1 , 5 ).

6. Consider the quadratic functions [pic] and [pic]. Find the equations of the two lines that are tangent to the graphs of both [pic] and [pic].

7. Find the equation of the parabola [pic] that passes through ( 0 , 1 ) and is tangent tot the line [pic] at ( 1 , 0 ).

8. Find the equation of the parabola [pic] that closely approximates [pic] at ( 1 , 0 ).

Hint: If a function “closely approximates” another, then the values of the functions and their first and second derivatives are equal at the given point.

-----------------------

y

[pic]

l

c

x

ANSWERS:

1) ( 7 , -209 ) , ( -1 , 7 )

2) [pic]

3) [pic]

4) ( -2 , .8 ) and ( 2/3 , 8/27 ) on [pic]

( 2/3 , -29/9 ) on [pic]

5) [pic]

6) [pic]

7) [pic]

8) h? ................
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