To find the slope of the tangent line to the parabola at a given point, we need to compute the derivative of our function first because it gives us the slope of the function at any point.
Our function is y = 3x^2 + 2x + 7.
The power rule for derivatives states that the derivative of x to the power of n is n times x to the power of (n-1). Using this rule, the derivative of 3x^2 is 6x, and the derivative of 2x is 2. As for the constant 7, the derivative of any constant is 0.
So, the derivative of the function y = 3x^2 + 2x + 7 is 6x + 2.
We want to find the slope of the tangent line at the point (2,23). To do this, we substitute the x-coordinate of the given point (which is 2) into the derivative.
This gives us 6*2 + 2, which simplifies to 12 + 2, and this equals 14.
Therefore, we conclude that the slope of the tangent line to the parabola y=3x^2 + 2x +7 at the point (2,23) is 14.