Calculus
posted by Leanna .
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)

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.
Respond to this Question
Similar Questions

calculus
A cubic polynomial function f is defined by f(x)= 4x^3+ab^2+bx+k where a, b, k, are constants. The function f has a local minimum at x=2 A. Fine the vales of a and b B. If you integrate f(x) dx =32 from o to 1, what is the value of … 
8th Grade Algebra
Multiply. 1) (3t^2  2t  4) * (5t + 9) Writing. 1) Explain why the product of a quadratic polynomial and a linear polynomial must be a cubic polynomial. 
Math:Polynomial Functions
h(x) = 7x I was thinking that this was not a polynomial function because 7x is just one term making it a monomial but the answer key says it is a polynomial function. Could someone explain why that is so? 
Calculus
A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? 
Calculus  Functions?
#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 … 
AP CALC. AB
2. A cubic function is a polynomial of degree 3 and has the form y=mx^3+bx^2+cx+d; m≠0. What is the maximum quantity of local extreme values a given cubic function can have? 
algebra
A cubic polynomial function f(x) has leading coefficient 2 and intercepts the yaxis at 2. If f(1)=1, and f(2)=2, find f(1) and write the complete function. 
Whats the answer
Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms. 211x^28x+6x^2. A) 5x^28x+2; quadratic trinomial B) 5x^28x; quadratic binomial C) 6x^28x2; cubic polynomial D) 8x+2; … 
math
A polynomial function function is defined by the equation p(x)=3x3+ax2+bx+7, where a, bE/. If p(2)=5 and p(1)=14 then the value of a+b is... 
Math Help TIMED!
write the polynomial in standard form then name the polynomial based on its degree and number of terms 10 g  7 g^3 + 2g^2  5 a. 7g^3 + 2g^2 + 10g  5 cubic polynomial b. 5 + 10g + 2g^2  7g^3 cubic binomial c. 7g^3  2g^2 + 10g …