Question

partner problem #9
find the slope of tangent line to curve (f(x)= - 2x^{3}+4x^{2}+3)

Explanation:

Step1: Differentiate the function

The derivative of $y = - 2x^{3}+4x^{2}+3$ using the power - rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$ is $y^\prime=-6x^{2}+8x$. The derivative of a function at a point gives the slope of the tangent line to the curve of the function at that point. Since no specific point is given, the general formula for the slope of the tangent line is the derivative of the function.

Answer:

The slope of the tangent line is $m=-6x^{2}+8x$