One definition of the derivative of a function f at a



MATH 160 Concept Quiz Name: ______________________________

Date: ________________ MATH 160 sec. ______

Time limit: 15 min. (5 min. collaboration, 10 min. writing) Calculator: Not allowed.

One definition of the derivative of a function f at a

number c is f'(c) =[pic][pic].

The figure shows the graph of a function y = f(x) and

a number c marked on the x-axis.

1. Illustrate and label each of the following quantities that appear in this definition on the graph. (You may assume h > 0.) Then write a short statement explaining in terms of the figure what each quantity means.

(a) f(c)

(b) h | x

c

(c) f(c+h)

(d) [pic]

(b) Explain in terms of tangent and secant lines what the equation f'(c) =[pic][pic] means.

Include an explanation of what the symbol [pic] means and why it is needed.

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