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I was asked to find the average gradient between $x=2$ and $x=5$ on the curve $y=x^2+3$.

My method:

Average gradient = $\frac{f(x+h)-f(x)}{h}$ $$=\frac{x^2+2xh+h^2+3-(x^2+3)}{h}$$ $$=\frac{h^2+2xh}{h}$$ $$ = 2x+h$$

What must I put in place of x? $5$ or $2$? and what must I put for the $h$ value? And why? Please help.

Note: Please do not give alternative solutions. Just elaborate on mine.

Aspiring Mathlete
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1 Answers1

5

You want $h=(5-2)=3$, $x=2$. This is so that $x+h=5$.

For average gradient one usually prefers the formula $$\frac{f(x_2)-f(x_1)}{x_2-x_1}$$ which makes it clear that

$$\frac{5^2+3-2^2-3}{5-2} =\frac{28-7}{3}=\frac{21}{3}=7$$

Shinaolord
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vadim123
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