Calc
posted by UCI STUDENT .
Use the Intermediate Value Theorem to check whether the equation x^3–3x+2.1=0 has a root in the interval (0,1)
answer: yes or no ?
i have no idea how to answer to go about solving this question, thanks for the help!

if x = 0 the function is 2.1
if x = 1 , the function is 0.1
so it does not necessarily cross the x axis between those points
If it does cross, it must cross twice to go from + to  to + again
so it would have to have a slope of zero in between there
df/dx = 3 x^2 3
0 = x^2  1
x= +1 or 1 for 0 slope
so it has no zero slope points between 0 and 1
So
It never crosses the x axis between 0 and 1
Respond to this Question
Similar Questions

calculus
Use the Intermediate Value Theorem to show that there is a root in the equation x^(1/3)=1x in the interval (0,1). 
calculus
Verify that the Intermediate Value theorem applies to the indicated interval and find the value of c guaranteed by the theorem. f(x) = x^2  6x + 8, [0,3], f(c) = 0 I have no idea how to use the theorem :( 
calculus
Use the Intermediate Value Theorem to prove that the equation has a solution. Then use a graphing calculator or computer grapher to solve the equation. 2x^32x^22x+1=0 i am completely lost & have no idea where to start. 
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? 
Math
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. x^4+x3=0, interval (1,2). According the to theorem, I found that a is 1, b is 2 and N is 0. f(1)= 2 and f(2) = 17. Is … 
Math
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. cos x = x. How do I begin this problem? 
math
Suppose f(x) = x^3 on the interval [1, 4]. Use the Mean Value Theorem to find all values c in the open interval (1, 4) such that f'(c)= (f(4)f(1))/41 c= square root of 7 c= cubed root of 21 c = 7 Mean Value Theorem does not apply 
Math
Let f(x) = 2x + 1 − sin(x), how many roots does f(x) have in the interval [−π, π]? 
Calculus
1. Use the Mean Value Theorem to find an xvalue where the instantaneous slope=average slope over the given interval: f(x)=(9x^2)^(1/2) on [3,2] I have done three chapters of Calculus already and I never have had to check for extraneous …