Answer
The slope at the point $(1, -1)$ is $8$.
Work Step by Step
The function is the sum of "smaller" functions hence the overall derivative is the sum of the derivative of the smaller functions.
The derivative of $2x^4$, using the power rule$((x^n)'=nx^{n-1})$, is $(2)(4)(x^{4-1})$ which when simplified is equal to $8x^3$.
The derivative of $-3$ is 0.
The overall derivative is therefore equal to $8x^3$.
To evaluate the derivative substitute in the x-coordinate. Plugging in $1$ gives $(8)(1)$ which is equal to $8$.
