Complete the table of values for \(y=\dfrac{x^2}{7}+\dfrac2x-2\). Give your answer to 2 decimal places.
| \(x\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) |
|---|
| \(y\) | \(0.14\) | \(-0.42\) | | \(0.79\) | \(1.97\) | \(3.48\) |
Complete the table.[1]
Using a scale of 2 cm to 1 unit, draw a horizontal \(x\)-axis for \(0<x\leq6\). Using a scale of 4 cm to 1 unit, draw a vertical \(y\)-axis for \(-1\leq y\leq5\). Plot the points given in the table and join them with a smooth curve.[3]
Use your graph to explain why the equation \(\dfrac{x^2}{7}+\dfrac2x-2=0\) has two solutions for \(0<x\leq6\).[1]
By drawing a tangent, find the gradient of the curve at \((4,0.79)\).[2]
By drawing a suitable straight line on the grid, solve the equation \(x^3+7x^2-28x+14=0\).[3]