Question

verfied the mean values theorm f(x) ) = x^2 in [1 , 1]​

Answer 1

Step-by-step explanation:

f(x)=x

2

in interval [2,4].

Now, checking the conditions for mean value theorem

Since, f(x) is a polynomial, it is continuous in (2,4).

Also, it is differentiable in (2,4).

Now, a=2 and b=4

f(a)=f(2)=4

f(b)=f(4)=16

f(x)=x

2

f

′

(x)=2x

f

′

(c)=2c

Now,

f

′

(c)=

b−a

f(b)−f(a)

2c=

4−2

16−4

2c=6

c=3

c=3∈(2,4)

Hence, Mean value theorem is satisfied.