Wednesday

April 23, 2014

April 23, 2014

Posted by **Jen** on Sunday, November 5, 2006 at 8:55pm.

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 function at each point. That is put the value of x as -2, -1.9,-1.8......-1. Look for changes in sign. That is the value of function should change signs, if this happens only once, then the function has only one solution in the interval. The values of x^4 + 3x + 1 at -2, -1.9, -1.8.......-1 are 11, 8.33,6.09, 4.25,2.75,1.56,0.6416,-0.0439,-0.53,-0.84,-1. Its very clear that the sign change occurs only once when X transitions from -1.4 to -1.3 so there is only one solution in this range which is between -1.4 and -1.3. This is however not an exact method.

The exact method would be to show first that the function is monotoniaclly increasing or monotonically decreasing and then show that the function takes a value of 0 in this interval. To do this you need to use calculus.

Yes, calculus is what I want to use!

This is from the chapter "application of derivatives".

Using mean value theorem how can i explain this? Thanks.

**Related Questions**

Calculas HS - show that the solution has exactly one solution in the interval x+...

Calculus - Solve the following initial value problem and determine the interval ...

Algebra - Solve and express in interval notation Solve: |5 – 8x| > 11 and ...

Math Help Please - Please show me how to put this in interval notation. Thanks! ...

Algebra - Just wondering if I did this correctly step by step. If not ...

algebra - for the system of inequalities y >= 2x - 1 and y <= 3x - 1, ...

algebra - for the system of inequalities y >= 2x - 1 and y <= 3x - 1, ...

algebra - Which has a Unique solution, No solution, or infinitely many ...

algebra 1 help - 5) give one solution to the inequality 12x-3x+11<4x-(17-9x...

Differential Equations - Consider the differential equation: dy/dt=y/t^2 a) Show...