Find the answer first using the deriavtive of the polynomial function.

Q: Determine the slope of the tangent to the graph of y = 6x^4 +2x^3 +5 at the point (-1,-3)

The slope of the tangent line at that point will be the derivative equation of the graph evaluated at that point.

A) Differentiating with respect to x gives: dy/dx = 24x^3 + 6x^2. Evaluating this equation at (-1,3) gives a slope of -24 +6 = -18.

The equation of the tangent line will be of the form: y = dy/dx*x + yo.

The y - intercept can be found through the equation (y-yo)/(x-0)=slope.

yo=y-x*dy/dx -> yo= 3+1*-18=-15.

Therefore the tangent line equation at (-1,3) is y = -18x - 15.