question 7\nin which of the following is the definition of the derivative correctly stated?\nchoose all that…

question 7\nin which of the following is the definition of the derivative correctly stated?\nchoose all that apply.\ninstantaneous rate of change\nslope of the tangent line\nlim_{h→0} \\frac{f(x + h)-f(x)}{h}\nslope of the secant line\naverage rate of change

question 7\nin which of the following is the definition of the derivative correctly stated?\nchoose all that apply.\ninstantaneous rate of change\nslope of the tangent line\nlim_{h→0} \\frac{f(x + h)-f(x)}{h}\nslope of the secant line\naverage rate of change

Answer

Brief Explanations:

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 $\lim_{h\rightarrow0}\frac{f(x + h)-f(x)}{h}$. 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
  • $\lim_{h\rightarrow0}\frac{f(x + h)-f(x)}{h}$