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August 22, 2014

August 22, 2014

Posted by **Amy** on Monday, February 21, 2011 at 6:14pm.

where a, b and k are constants. The function f has a local minimum at x = -1, and the graph of f has a point of inflection at x= -2

a.) Find the values of a and b

#2. Let h be a function defined for all x (not equal to) 0, such that h(4) = -3 and the derivative of h is given by h'(x) = (x^2 - 2) / (x) for all x (not equal to) 0.

a.) Find all values of x for which the graph of h has a horizontal tangent, and determine whether h has a local maximum, a local minimum, or neither at each of these values. Justify your answers.

b.) On what intervals, if any, is the graph of h concave up? Justify

c.) Write an equation for the line tangent to the graph of h at x=4

d.) Does the line tangent to the graph of h at x = 4 lie above or below the graph of h for x > 4 ? Why?

- Calculus - Functions? -
**Reiny**, Monday, February 21, 2011 at 6:59pmI will do #1 for you.

Show some work or steps that you have done for #2 and#4 and I will evaluate your work.

#1:

f '(x) = 12x^2 + 2ax + b

f ''(x) = 24x + 2a

f '(-1) = 0 = 12 - 2a +b ---> 2a - b = 12

f ''(-2) = 0 = -48 + 2a ----> a= 24

then 2(24) - b = 12

b = 36

a = 24 , b = 36

- Calculus - Functions? -
**bob**, Thursday, January 31, 2013 at 3:29pma billion

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