- Let \(f(x) = 2x^9 - 3x - 2\). Write a complete sentence referring to the intermediate value theorem that proves that \(f\) has a root in the interval \([0,2]\).
- Let \(f(x) = 5x^2\). Write down the difference quotient \[
\frac{f(x+h) - f(x)}{h}
\] for this function. Then simplify the expression by expanding the numerator and performing any cancellations that you see.
- The complete graph of a function \(f\) is shown on the reverse, together with a pair of axes below the graph. Draw the graph of the derivative \(f'\) of \(f\) on the lower set of axes.
