Post-Video Questions Preview

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Here are some questions you’ll be asked after you finish watching the videos. Please read through these before watching the videos.

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 $f$ ?