Math 161 Calculus I

Reading Outlines

You should answer these questions as you read the text.

Section 3.4

1. What is (sin x)'? How about (cos x)'?
2. Explain why the graphs give evidence for the derivatives above.
3. On the graph of sin x, what is represented by $\lim_{h\rightarrow 0}^{}$${\frac{\sin h}{h}}$?
4. On the graph of cos x, what is represented by $\lim_{h\rightarrow 0}^{}$${\frac{\cos h - 1}{h}}$?
5. If f (x) is just a horizontal shift of g(x) (that is, f (x) = g(x + a) for every x), then how are the slopes of f and g related? Fill in the blank: f'(x) =  
6. Each of the other trig functions besides sin and cos is an algebraic combination of the others. Why can't we just use that fact to compute their derivatives?
7. What's the antiderivative of sin x? Of cos x? How many functions are there whose derivative is sin x?
8. Is every stationary point of a function either a minimum or a maximum? How can you tell which one it is?