Across
- 2. valleys
- 3. a function is _______ if f(c) is defined, the limit as x approaches c f(x) exists, and f(c)=the limit as x approaches c f(x)
- 7. refers to the rate of change (derivative)
- 8. the derivative of the outside, leave the inside alone, times the derivative of the inside
- 9. states that there is a line tangent to the curve at some point that has the same slope as the secant line
- 11. a line the function almost touches, but never does
- 13. deciding what quantity to be maximized or minimized in terms of only one variable
- 15. used as a form of solving for x if it cannot be factored
- 16. d/dx (f(x)times g(x))= f'(x) times g(x)+f(x) times g'(x)
- 17. when f(x) becomes arbitrarily close to a unique number as x approaches c from either side
- 18. d/dx (f(x)+or-g(x))
- 21. d/dx (lnx) = 1/x
- 24. when f''(x)=0
- 25. the derivative of any constant is 0
- 26. marginal revenue - marginal cost
- 27. d/dx (c times x^n) = c times nx^n-1
- 28. hills
- 29. graph is frowning (f''(x)<0)
Down
- 1. the slope of a line tangent to a curve at any point
- 3. a way of finding limits by factoring, then cancelling and plugging in x
- 4. can describe a limit that does not exist
- 5. states that if f satisfies the conditions of the theorem, then there must be at least 1 point between a and b at which f'(x)=0
- 6. used mostly to determine if there is a zero of the function on an indicated interval
- 10. along the x-axis
- 12. holes, asymptotes, and jumps
- 14. a way of finding limits by plugging in x
- 19. when the derivative is either zero or undefined
- 20. used when limits end in an indeterminate form
- 22. graph is smiling (f''(x)>0)
- 23. the derivative of x to n power is n times x to the n-1