Question

Find the maximum/minimum value of the quadratic expression $-x^2+8x+1$

• A. Minimum value is $17$
• B. Minimum value is $-34$
• C. Maximum value is $17$
• D. Maximum value is $34$

Answer 1

The correct option is C Maximum value is $17$

$f\left(x\right)=-x^2+8x+1$

$\text{Simce,}a<0$

$\text{It is downward porabola}$

$f^{\prime }\left(x\right)=-2x+8$

$\Rightarrow 0=-2x+8$

$\Rightarrow 2x=8$

$\therefore x=4$

$f^{\prime \prime }\left(x\right)=-2<0$

$\text{Maxima occurs.}$

$f\left(4\right)=\text{Max. ralue}$

$=-4^2+8\times 4+1$

$=-16+32+1$

$=17$