Across
- 2. If f ‘(c)=0 and f “(x)<0, then f has a ______ at x=c
- 5. If f’ does not change sign at c (f’ has the same sign on both sides of c) then f has no local ____ value.
- 7. if function f(x) has a derivative, it is ______
- 9. if f “(x)>0
- 12. the process of finding a curve to fit data
- 13. rule f(x)=x^n , f ‘(x)=nx^n-1
- 14. problems involving the relationship between two or more rates
- 15. Calculator function used to find derivative
- 16. F=kx
- 21. “The limit does not exist!!”
- 24. [a,b]
- 28. a^2+b^2=c^2
- 32. when a function is differentiable at a point a that closely resembles its own tangent line very close to a
- 33. The largest segment of a partition
- 36. another name for the Fundamental Theorem of Calculus
- 44. Deriving an equation with two variables is __________ differentiation
- 48. If the function is concave down and you are finding LRAM, the area under the curve is a _______
- 49. Find y’ of y=ln(secx+tanx)
- 51. when marginal revenue equals marginal cost
- 53. The definite integral of the force times distance over which the force is applied
- 54. the function reflected over the line y=x
- 55. Suppose u and v are functions of x that are differentiable at x=0, and that u(0)=5, u‘(0)= -3, v(0)= -1, v’(0)=2. Find d/dx(uv)
- 56. The ______ dx is an independent variable and the _____ dy = f ‘(x)dx
- 57. notation
- 58. Absolute value of position
Down
- 1. instantaneous rate of change
- 3. This is an example of f(x)=cos(x^3); f ’(x)= -3x^2(sin(x^3))
- 4. The third derivative of position
- 5. y=y0e^kt
- 6. If velocity is positive and speed is decreasing, then acceleration is _____
- 8. where the function is continuous but not differentiable
- 10. (LRAM+RRAM)/2)=
- 11. the line about which a solid of revolution is generated
- 17. a point near which the function values oscillate too much for the function to have a limit
- 18. a function y=f(x) that is continuous on [a,b] takes on every value between f(a) and f(b)
- 19. Δx=x2-x1 and Δy=y2-y1
- 20. (a,b)
- 22. If velocity is positive and decreasing, then speed is _____
- 23. (ln2/k)
- 25. if f ‘(x)=(1/(1+x^2)), then f(x)=?
- 26. ln(x/x)=?
- 27. Reimann sum using midpoints
- 28. (2π/b) describes this
- 29. ∆f=f(a+dx)-f(a)
- 30. when maximizing or minimizing some aspect of the system being modified
- 31. ((absolute max of f-absolute min of f)/2)
- 32. L(x)=f(a)+f ‘(a)(x-a)
- 34. y=mx+b
- 35. where one-sided limits exist but have different values
- 37. the easiest way to do separation by parts
- 38. (∆x/∆t)
- 39. Change in concavity
- 40. T-Ts=(T0-Ts)e^-kt
- 41. Application of local linearity used to graph a solution without knowing its equation
- 42. If a function is continuous on [a,b] and differentiable on (a,b), then there exists a point c on (a,b) where f ‘(x)=((f(b)-f(a))/(b-a))
- 43. theorem
- 45. LRAM,MRAM,RRAM
- 46. If f “(x)>0 and you are finding LRAM, its an _____
- 47. a point that is extremely essential ( if f ‘(x)=0, where x=?)
- 50. circle with radius of 1
- 52. the length of a rectangle increases by 5 cm/sec and the width decreases by 2 cm/sec. Is the area increasing or decreasing when length=7 cm and width=4 cm