Final answer:
The slope of a polynomial curve at a given point can be calculated using the derivative of the function. The correct option is a) f'(x).
Step-by-step explanation:
To calculate the slope of a polynomial curve at a given point, we need to find the derivative of the polynomial function. The derivative represents the rate of change of the function at a specific point. The options given are:
a) f'(x) - this represents the first derivative of the function, which gives the slope of the curve at any given point.
b) f''(x) - this represents the second derivative of the function, which gives the rate of change of the slope.
c) f(x) - this represents the polynomial function itself, not its slope.
d) f⁻¹(x) - this represents the inverse of the function, not its slope.
Since we are looking for the slope, the correct option is a) f'(x). This will give us the slope of the curve at the given point.