Calculus
posted by David .
a) prove that the function x^3 + 9x^2 +33x assumes the value 8 at least once
b)using the mean value theorom or rolle's theorom  no other methods will be accepted  prove carefully that x^3 + 9x^2 + 33x takes on the value 8 at most once

Calculus 
MathMate
a.
determine the domain and range of the function and conclude.
b.
Prove by contradiction:
assume that there are two or more values of x for which f(x1)=8 and f(x2)=8, where x1<x2.
Consider the interval [x1,x2], and apply Rolle's theorem or the mean value theorem to see if it is possible to find such x1, x2.
Respond to this Question
Similar Questions

unique solution
How do I show that the equation x^4 + 3x + 1 = 0, 2 <= x <= 1 has exactly one solution in the interval. Thanks. One way to do this is to use trial and error. split the interval (2,1) into 10 equal parts. Then evaluate the … 
maths
prove that 1+x < e^x < 1+ xe^x for x>0 using the mean value theorem 
Calculus
Suppose f(x) = x ^ 4 – 4x ^ 2 + 6, and g(x) = 3x ^ 3 – 8x. Prove, via the Intermediate Value Theorem, that the functions intersect at least twice between x = –2 and x = 4. 
Math  Calculus
Show that the equation x^315x+c=0 has at most one root in the interval [2,2]. Perhaps Rolle's Theorem, Mean Value Theorem, or Intermediate Value Theorem hold clues? 
Math  Calculus
Show that the equation x^315x+c=0 has at most one root in the interval [2,2]. Perhaps Rolle's Theorem, Mean Value Theorem, or Intermediate Value Theorem hold clues? 
Calculus I
Show that the equation x^4 + 4x + c = 0 has at most two real roots. I believe we're supposed to prove this by proof of contradiction using Rolle's Theorem, but I'm not quite sure how to do this problem. 
MATH
How can i know the result ofdivision 3x^2+6x4 with 5x+2 in factor theorom 
mathscalculus
mean value theorem prove sq root 9.1 is less than or equal to 3+1/60 
geometry
what is the diffwereence between a postulate and theorom 
physics
Compare the slope of the velocitytime graph to the average of all your acceleration values. Are they close?