Question

Show that the equation x^3+6x-5=0 has a solution between x=0 and x=1

Answer 1

Answer:

Since the value of f(0) is negative and the value of f(1) is positive, then there is at least one value of x between 0 and 1 for which f(x) =0.

Step-by-step explanation:

The equation f(x) given is:

$f(x) = x^3+6x-5$

For x = 0. the value of the expression is:

$f(0) = 0^3+0-5\\f(0) = -5$

For x = 1, the value of the expression is:

$f(1) = 1^3+6-5\\f(1)=2$

Since the value of f(0) is negative and the value of f(1) is positive, then there is at least one value of x between 0 and 1 for which f(x) =0.

In other words, there is at least one solution for the equation between x=0 and x=1.