Posted by **Leanna** on Wednesday, February 9, 2011 at 6:39am.

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

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

b) If ∫ (from 0 to 1) f(x) dx = 32, what is the value of k?

I found a=24 and b=36

i don't know about B)

- Calculus -
**MathMate**, Wednesday, February 9, 2011 at 6:56am
From a=24,b=36,

we find

f'(x)=0 has roots at x=-3 and -1, so that checks.

f"(x)=0 has a root at x=-2, so that checks too.

To solve B, we integrate

f(x):=4*x^3+24*x^2+36*x+k

from 0 to 1:

I=∫f(x)dx

=x^4+8*x^3+18*x^2+k*x

Evaluate I from 0 to 1 to give k+27

But since is given as I=32, so

I=32=k+27

Solve for k.

## 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+ab^2+bx+k ...
- Calculus - Functions? - #1. A cubic polynomial function f is defined by f(x) = ...
- AP CALC. AB - 2. A cubic function is a polynomial of degree 3 and has the form y...
- algebra - A cubic polynomial function f(x) has leading coefficient -2 and ...
- 8th Grade Algebra - Multiply. 1) (3t^2 - 2t - 4) * (5t + 9) Writing. 1) Explain ...
- Math:Polynomial Functions - h(x) = -7x I was thinking that this was not a ...
- algebra - What is cubic polynomial function in standard form with zero 1, -2, ...
- Math - The function f(x) = x^2 -2x + x^1/2 is: A. A polynomial because it is ...
- Pre-Calculus - Graphing Polynomials Decide whether each of the following is ...

More Related Questions