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

#1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k

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?

## Answer this Question

## Related Questions

- Calculus - A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx...
- Calculus - A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx...
- calculus - A cubic polynomial function f is defined by f(x)= 4x^3+ab^2+bx+k ...
- AP CALC. AB - 2. A cubic function is a polynomial of degree 3 and has the form y...
- Calculus - Find constants a and b in the function f(x)=axbln(x) such that f(15...
- Calculus - Find constants a and b in the function f(x)=(ax^b)ln(x) such that f(...
- calculus - Find constants a and b in the function f(x)=ax^b/(ln(x)) such that f(...
- Calculus 1 - Find constants a and b in the equation f(x)= ax^b/(ln(x)) such ...
- Calculus - Find constants a and b in the equation f(x)= ax^b/(ln(x)) such that f...
- Trig - The polynomial function f(x) is defined by f(x)=-4x^4+9x^3+2x^2-7x-2. Use...

More Related Questions