Practice: Exactly One Root

Related Topics

Wize University Calculus 1 Textbook > Applications of Differentiation

Rolle's Theorem

3 Activities

checklist

Mark Yourself Question

Grab a piece of paper and try this problem yourself.
When you're done, check the "I have answered this question" box below.
View the solution and report whether you got it right or wrong.

 
Q.\textbf{Q.}Q. Show that the equation x+sin⁡x=1x+\sin{x}=1x+sinx=1 has exactly one solution in the interval [0,1][0,1][0,1]. 

I have answered this question

More Rolle's Theorem Questions:

Rolle's Theorem

The function f(x)=1x2f(x) = \frac{1}{x^2}f(x)=x21​ has no horizontal tangent lines on the interval [−1,1][-1,1][−1,1] , even though f(−1)=f(1)f(-1)=f(1)f(−1)=f(1). Why doesn't this contradict Rolle's Theorem?

Prove that f(x)=x3−6x2+11x+5f(x)=x^3-6x^2+11x+5 f(x)=x3−6x2+11x+5 has exactly one zero on the interval [−1,1][-1,1][−1,1]. 

Rolle's Theorem: Exactly One Solution

Show that the equation cos⁡2(x)=2x\cos^2(x)=2xcos2(x)=2x has exactly one solution on R\mathbb{R}R.