find the slope of the line that is tangent to the curve y=-3x^2+5x-11 at x=-4

To find the slope of the line that is tangent to the curve at a given point, we need to find the derivative of the function at that point. The derivative of a function gives us the slope of the tangent line at any point on the curve.

The given function is y = -3x^2 + 5x - 11.

Step 1: Find the derivative of the function. The derivative of y = -3x^2 + 5x - 11 is y' = -6x + 5.

Step 2: Substitute the given x-value into the derivative. Substitute x = -4 into y' = -6x + 5 to find the slope of the tangent line at x = -4. y' = -6(-4) + 5 = 24 + 5 = 29.

So, the slope of the line that is tangent to the curve y = -3x^2 + 5x - 11 at x = -4 is 29.