Question

What is the slope of the function `y = a + 2bx^2` ?

Answer 1

The slope of the tangent at any particular `x`-coordinate is given by the `4bx`.

Explanation:

This is not a particularly well worded question The given curve represents a quadratic function and therefore the "slope" of the function does not exist as we can only measure the slope of a straight line.

Instead we can consider the slope of the tangent to the curve at any particular given point, and this is given by the derivative:

We have:

`y = a + 2bx^2`

Differentiating wrt `x` we get:

`dy/dx = 4bx`

Hence, the slope of the tangent at any particular `x`-coordinate is given by the `4bx`.