Post Video Questions

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Please answer each of these questions to the best of your ability. You are welcome to re-watch parts of any of the videos to help you.

The slope of the line tangent to the graph of $y = f(x)$ at the input value $x = 5$ is shown in the graph below. The slope of this tangent line is $0.712$ .

Which of the following statements most accurately conveys what happens to the value of $f(x)$ as the value of $x$ varies by an infinitesimal amount $dx$ away from $x = 5$ ?

The value of $f(x)$ changes by $0.712$ . The value of $f(x)$ changes by $0.712$ times $5$ . The value of $f(x)$ changes by $0.712$ divided by $5$ . The value of $f(x)$ changes by $0.712$ times $dx$ . The value of $f(x)$ changes by $0.712$ divided by $dx$ .

Suppose $f'(a)<\dfrac {f(a+\Delta x) - f(a)}{\Delta x}$ for $\Delta x > 0$ . Which of the following could be the graph of $f$ ?

I only II only I and III only II and III only III and IV only