BC Free Response #4
BC calculus free response questions
A. To determine where the relative maximum and the relative minimum is you must set the equation of the derivative to 0.  This will allow you to determine the crticial point values of the graph.  After you solve this you will get an answer of negative root 2 and postive root 2.  The minimum will be at x=-root 2 and the maximum will be at positive root 2.

B. To determine the concavity you must use the second derivative of the function.  The second derivative of h(x) is [(x^2)+2]/x^2.  Since this can only be positive the function will be concave up always EXCEPT when x=0 because this is where the function is undefined.

C. To find the tangent line at x=4, you can simply plug in 4 in the h'(x) and this will give you the slope of (7/2) at point (4,-3).  You can then find the equation since you have the points and the slope:     
y-(-3)=(7/2)(x-4)
y+3=(7x/2)-14
y=(7x/2)-17                        

D. Because the concavity of the curve is up the tangent line must lie beneath the curve.
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