Question

100pts: What is the slope of the following curve at x = n, for an arbitrarily chosen integer n?:

y = 3x^2 - 37x + 6

Answer 1

6n - 37

Explanation:

The derivative of the function f(x) gives the gradient (slope) of the tangent to the graph of y = f(x) at the point (x, y).

Given:

`y=3x^2-37x+6`

Therefore, the gradient (slope) of the given curve at x is:

`\implies (dy)/(dx)=2 \cdot 3x^(2-1)-37x^(1-1)+0`

`\implies (dy)/(dx)=6x-37`

To find the slope, simply substitute x for n:

`\implies 6n-37`

Answer 2

6n -37

Explanation:

The slope would be the derivative of the function

dy/dx = 6x - 37 evaluated at the point n

dy/dx = 6n -37