Verify Lagranges mean value theorem for function `f(x)=x^2+x-1` on `[0,\ 4]` and find a point `' c '` in the indicated interval:

Explanation

Given, `f(x)=x^2+x-1` is continuous on `[0,\ 4]` and differentiable on `(0,\ 4)`. Since, it is polynomial function.


`f'(c)=(f(b)-f(a))/(b-a)`


`f(x)=x^2+x-1`


`f'(x)=2x+1`


`f'(c)=2c+1=(16+4-1+1)/(4-0)`


`2c+1=5`


`c=2 in (0,4)`


LMUT is verified