Practicing Success
Let $f(x)=x^2+x g'(1)+g''(2)$ and, $g(x)=x^2+x f'(2)+f''$ (3). Then, |
$f'(1)=4+f'(2)$ $g'(2)=8+g'(1)$ $g''(2)+f''(3)=4$ all the above |
all the above |
We have, $f(x)=x^2+x g'(1)+g''(2)$ and $g(x)=x^2+x f'(2)+f''(3)$ $\Rightarrow f'(x)=2 x+g'(1)$ and $g'(x)=2 x+f'(2)$ ........(i) Putting x = 1 in (i), we get $f'(1)=2+g'(1)$ and $g'(1)=2+f'(2)$ $\Rightarrow f'(1)=4+f'(2)$ Putting x = 2 in (i), we get $f'(2) =4+g'(1)$ and $g'(2)=4+f'(2)$ $\Rightarrow g'(2)=4+4+g'(1)=8+g'(1)$ Differentiating (i) w.r.t. x, we get $f''(x)=2$ and $g''(x)=2$ for all x $\Rightarrow f''(3)=2$ and $g''(2)=2$ $\Rightarrow g''(2)+f''(3)=2+2=4$ |