Question

The gradient of the line joining the points on the curve $y=x^2+2x$ whose abscissa are $1$ and $3$, is

• A. $6$
• B. $5$
• C. $4$
• D. $3$

Answer 1

The correct option is A

$6$

Explanation of the correct option.

Compute the gradient.

Given : $y=x^2+2x$.

The abscissa are $1$ and $3$.

When $x=1$,

$y=1^2+2$

$\Rightarrow$ $y=3$

When $x=3$,
$y=3^2+6$

$\Rightarrow$ $y=15$

So the points are $(1,3)$ and $(3,15)$.

Gradient $=\frac{(y_2–y_1)}{(x_2–x_1)}$

$\Rightarrow$ gradient$=\frac{(15–3)}{(3–1)}$

$\Rightarrow$ gradient$=\frac{12}{2}$

$\Rightarrow$ gradient$=6$

Hence option $A$ is the correct answer.