Question

If $f(x)=ax^{2}+6x+5$ attains its maximum value at $x=1$, then the value of a is ________.

• A. 0
• B. 5
• C. 3
• D. -3

Hint:

For a parabola $ax^2+bx+c$, vertex occurs at $x = -b/2a$.

Answer 1

The Correct Option is D

Step 1: Concept
Maxima occurs when $f'(x) = 0$ and $f''(x)<0$.
Step 2: Analysis
$f'(x) = 2ax + 6$.
Setting $f'(1) = 0$ because max is at $x=1$.
Step 3: Calculation
$2a(1) + 6 = 0 \Rightarrow 2a = -6 \Rightarrow a = -3$.
Step 4: Verification
$f''(x) = 2a = 2(-3) = -6$, which is negative. This confirms a maximum.
Final Answer:(D)