Homework Help: calculus

Posted by Equihua on Friday, January 4, 2013 at 2:38pm.

Let g be the function give by g(x) = x^4 - 4x^3 + 6x^2 – 4x + k where k is constant.
A.On what intervals is g increasing? Justify your answer.
B.On what interval is g concave upward? Justify your answer.
C.Find the value of k for which g has 5 as its relative minimum. Justify your answer.

calculus - Steve, Friday, January 4, 2013 at 3:10pm
g = x^4 - 4x^3 + 6x^2 – 4x + k
g' = 4x^3 - 12x^2 + 12x - 4 = 4(x-1)^3
g'' = 12x^2 - 24x + 12 = 12(x-1)^2

g increasing where g' > 0: x>1
g concave up where g'' > 0: all real x

g(x) = (x-1)^4 + (k-1)
so, if g(1) = 5, k=6

Answer this Question

Related Questions

math-calculus - i think i do something wrong again(2x+1)/(x-3)-(4x-1)/(2x-3) = 0...
Calculus - Use the algorithm for curve sketching to sketch the graph of each ...
Simplifying Rational Expressions - Can someone slove these for me 1.(4x-12)/4x 2...
Math - Can someone please check my answers below for accurateness? The ...
Simplifying Rational Expressions - Can someone PLEASE solve these for me 1.4x-12...
Math - Find the following function y=[(x-5)(4x+3)]^5 I arrived at 5(6x-2)[(x-5)(...
Algebra2 - Complete parts a – c for each quadratic function: a. Find the y-...
math correction - Directions: Perform the indicated divisions. The problem: (8x^...
math-calculus - 4x+3/2x-1-2 = 6x+2/2x-1 (4x+3)(-2) = (6x+2) -8x-6 = 6x+2 -14x-6...
Math - First, give the technology formula for the given function and then use ...

For Further Reading

First Name:
School Subject:
Answer: