Question

A curve f(x) has a property that the slope of the tangent to the curve:

a) Is constant for all values of x
b) Varies based on f(x)
c) Is always negative
d) Approaches infinity as x increases

Answer 1

The slope of the tangent to a curve can vary based on f(x).

Step-by-step explanation:

The slope of the tangent to a curve can change for different values of x, depending on the shape of the curve. It can be positive, negative, or zero. For example, consider the curves of the functions y = x^2 and y = -x^2. The slopes of the tangents to these curves will vary at different values of x.