Pre-Video Questions

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Before watching the videos, think about and answer these questions to the best of your ability.

The slope of the line tangent to the graph of $y = f(x)$ at the input value $x = 7$ is shown in the graph below. The slope of this tangent line is 1.

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 $x = 7$ ?

The value of $f(x)$ changes by 1. The value of $f(x)$ changes by 1 times 7. The value of $f(x)$ changes by 1 divided by 7. The value of $f(x)$ changes by 1 times $dx$ . The value of $f(x)$ changes by 1 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 II and III only I and IV only III and IV only

Overall, how confident are you in your answers?

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