Question

question 7
in which of the following is the definition of the derivative correctly stated?
choose all that apply.
instantaneous rate of change
slope of the tangent line
lim_{h→0} \frac{f(x + h)-f(x)}{h}
slope of the secant line
average rate of change

Explanation:

The derivative of a function represents the instantaneous rate of change of the function. Geometrically, it is the slope of the tangent line to the graph of the function at a given point. The limit definition of the derivative of a function $y = f(x)$ is $\lim_{h
ightarrow0}\frac{f(x + h)-f(x)}{h}$. The slope of the secant line and average rate of change are related to the difference - quotient but not the derivative. The derivative is about the limit as the interval shrinks to a point.

Answer:

• Instantaneous rate of change
• Slope of the tangent line
• $\lim_{h

ightarrow0}\frac{f(x + h)-f(x)}{h}$