Draw corresponding secant and tangent lines on the graph of a function

Question

Sketch the graph of a function f(x) that satisfies the following criteria. (You do not need to define the function

algebraically.)

1. Defined and continuous on the interval [-10, 10]
2. The rate of change of f(x) when x = -7 is negative
3. The slope tangent to the graph of f(x) at x = 9 is positive
4. the lim as h --> 0 (f(-9+h)-f(-9))/h does not exist
5. f'(x) = 0 at x = 4

Answer 1

Sharon,

"defined and continuous" means you can draw it without lifting your pencil

"rate of change is negative" means downhill (reading from left to right)

"slope of the tangent is positive" means uphill (reading from left to right)

"limit does not exist" for limit of difference quotient aka derivative means a corner, a "vee shape"

Please tell your teacher/professor that a tutor said his is a great, not good, but great question.

Hope this helps--Andrew F.