Question

question 8
in which of the following are the primary interpretations of the derivative correctly stated?
choose all that apply.
slope of the secant line
average rate of change
slope of the tangent line
instantaneous rate of change
$lim_{h
ightarrow0}\frac{f(x + h)-f(x)}{h}$

Explanation:

The derivative represents the slope of the tangent line to a curve at a point, which is also the instantaneous rate of change of a function. The limit definition $\lim_{h
ightarrow0}\frac{f(x + h)-f(x)}{h}$ is the formal definition of the derivative. The slope of the secant line and average rate of change are related to differences between two points on a curve, not the derivative.

Answer:

C. Slope of the tangent line
D. Instantaneous rate of change
E. $\lim_{h
ightarrow0}\frac{f(x + h)-f(x)}{h}$