LaGrange's Mean Value Theorem

Q. According to Lagrange's mean value theorem, given that all conditions are satisfied for f(x) in the interval $[a,b]$, there exists at least one c such that f'(c) = , where $a<c<b$

1. $\frac{f\left(b\right)-b}{f\left(a\right)-a}$
2. $\frac{f\left(b\right)-f\left(a\right)}{b-a}$
3. $\frac{f\left(a\right)-f\left(b\right)}{b-f\left(a\right)}$

Q.

How do you find the Rolles value theorem applies?

Q. f = {(a, 2) {(2, 4) {(2, 5) {(3, 9)}, is its function or not (T/F)

1. Uncertain
2. None of these
3. True
4. False

Q. Suppose f is a real function satisfying $f(x+f(x\left)\right)=4f\left(x\right)$ and $f\left(1\right)=4$. Find the value of $f\left(21\right)$.

1. $16$
2. $21$
3. $64$
4. $80$

Q.

Put $>,<$or $=$ in the boxes.

If $25\mathrm{m}=50$ then $6\mathrm{m}\boxed{}12$