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Find equations of the tangent lines at points

Given y = 3 + 4x^2 - 2x^3, how do I find the **slope** of the tangent line at point (1,5), for example, using the Newton Quotient Law or something in the Derivatives Chapter I'm studying. I "cheated" and estimated the slope by plugging in x = 1.01 and then finding the slope of between the points (1,5) and (1.01, 5.019798) but I'd like to be able to solve this the proper (and required) way. My work is attached.

Any help would be greatly appreciated!

Thanks in advance!