A radio dish is modelled by a family of parabolas with the axis along the x-axis and the vertex at…

Step 1. First derivative. $2yy' = 4a$, so $yy' = 2a$. The constant $b$ has already gone.

Step 2. Second derivative. The product rule gives $y'\cdot y' + y\cdot y'' = 0$. So

Step 3. Order and degree. The highest derivative is $y''$ and its power is $1$. The order is $2$ and the degree is $1$.

Step 4. The member. At $x = 3\ \text{m}$ we have $y^2 = 8 \times 4 = 32$, so $y = \sqrt{32} = 5.6569\ \text{m}$ on the upper branch. From $yy' = 2a = 4$ we get $y' = \dfrac{4}{5.6569} = 0.7071$.

Step 5. The second derivative. $y'' = -\dfrac{(y')^2}{y} = -\dfrac{0.5}{5.6569} = -0.0884$.