Mathematics 4024 · O Level · Graphs of functions

Graphs of functions — practice question

The function is $y=\dfrac{x}{20}(x^2-10)$.
(a)[1]

Fill in the table of values for $y=\dfrac{x}{20}(x^2-10)$.

(b)[2]

On axes using a scale of $2\text{ cm}$ to $1$ unit on both axes, sketch the graph of $y=\dfrac{x}{20}(x^2-10)$ for $0 \le x \le 5$.

(c)[2]

By drawing a tangent, estimate the gradient of the curve at the point where $x=2.5$.

(d)[2]

Use the graph to solve $\dfrac{x}{20}(x^2-10)=0$ for $0 \le x \le 5$.

(e(i))[2]

Find the equation of the straight line $L$ that is used with the graph of $y=\dfrac{x}{20}(x^2-10)$ to solve $x^3+10x-80=0$.

(e(ii))[1]

Draw the graph of line $L$ on the grid.

(e(iii))[1]

Hence solve the equation $x^3+10x-80=0$ for $0 \le x \le 5$.

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