Question

Find the value(s) of c guaranteed by Rolle's Theorem for f(x) = x sinx on the interval
[-3,3]. I found the derivatives but i dont understand how to fibd the zeros​

Answer 1

Answer:

The value of c is 0,-2.194 and 2.194 in the interval (-3,3).

Step-by-step explanation:

To find the value of c for a given function using Rolle's Theorem we have to find the first derivative of the function and then equate it to zero.

These solutions of x are the values of c.

f(x) = x sin(x)

$\frac{df}{dx}$ = xcosx + sinx

xcosx + sinx = 0

x = -tanx

Using the graphical method we can see that 0,-2.194 and 2.194 is a solution of the equation.There are infinitely many solutions but in the interval (-3,3) there is only 3 solution.