JAMB 2000 · UME · Q40

Calculus (JAMB bridge)

The expression $ax^2 + bx + c$ equals 5 at $x = 1$ . If its derivative is $2x + 1$ , what are the values of $a$ , $b$ , $c$ respectively?

Worked solution (try it first)

The derivative of $ax^2 + bx + c$ is $2ax + b$ .
Match it with $2x + 1$ : $2a = 2$ and $b = 1$ , so $a = 1$ and $b = 1$ .
At $x = 1$ the expression is $a + b + c = 5$ , so $1 + 1 + c = 5$ and $c = 3$ .
So $a$ , $b$ , $c$ are 1, 1, 3, option D.

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