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

1 Answer
Dec 6, 2017

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.