Question

If f(x) = ax² + bx + c, then f '(1) + f '(4) - f '(5) is equal to _____________________.

Answer 1

$f\left(x\right)=a{x}^2+bx+c$

$\therefore f\text{'}\left(x\right)=\frac{d}{dx}\left(a{x}^2+bx+c\right)$

$\Rightarrow f\text{'}\left(x\right)=2ax+b$

$\therefore f\text{'}\left(1\right)+f\text{'}\left(4\right)-f\text{'}\left(5\right)$

$=\left(2a\times 1+b\right)+\left(2a\times 4+b\right)-\left(2a\times 5+b\right)$

$=2a+b+8a+b-10a-b$

$=b$

Thus, the value of $f\text{'}\left(1\right)+f\text{'}\left(4\right)-f\text{'}\left(5\right)$ is b.

If f(x) = ax² + bx + c, then f '(1) + f '(4) − f '(5) is equal to ___b___.