Question

find c of the Cauchys mean value theorem for which
f(x) - roof of (25- x^2) in [1,5]​

Answer 1

Answer:

tuiefgokndjkoo

25245747834785468

Answer 2

Answer:

The given function f(x)=x  

2

(1−x  

2

) on [0,1] is continuous and differentiable on (0,1), since it is a polynomial of degree 4.

Again f(0)=0=f(1).

So f(x) satisfies all the conditions of Rolle's theorem.

According to Rolle's theorem there exists c∈(0,1) such that f  

′

(c)=0.

Now f  

′

(c)=0 gives

2c−4c  

3

=0

or, 2c(1−2c  

2

)=0

or, c=  

2

​  

 

1

​  

 [ Since c∈(0,1)]

Step-by-step explanation: