Question:
find the value of c in roll's theorem for the function f(x) = x*3 - 3x in [ - (3)*1/2, 0]
Answer:
Given, f(x) = x3 - 3x
Now, f{-(31/3 ) = -(31/2 )3 + 3 * (31/2 )
=> f{-(31/3 ) = -33/2 + 31/2 + 1
=> f{-(31/3 ) = -33/2 + 33/2 )
Again, f(0) = 0
Now, df(x)/dx = 0
=> 3x2 - 3 = 0
=> x2 - 1 = 0
=> (x - 1)*(x + 1) = 0
=> x = -1, 1
So, the value of c is ±1
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