Calculus MATH Practice Quiz
1. If (c, f(c)) is a point of inflection of the graph of f, then either f"(c)=0 or f"
is undefined at c
Answer: Points of Inflection
2. Where first derivative is 0 or undefined
Answer: Critical Value
3. Use critical values and END POINTS in the function
Answer: Find absolute extrema
4. If m>n: NO HA
If m=n: HA = co-eff of m/co-eff of n
If m<n: HA: y = 0
Answer: Horizontal Asymptote Rules
5. If f(x) is continuous on [a,b] and differentiable on (a,b), there is at least one
point (x=c) where f'(c)= F(b)-F(a)/b-a
Answer: Mean Value Theorem
6. If f is continuous on [a,b] then f has an absolute maximum and an absolute
minimum on [a,b]. The global extrema occurs at critical points in the interval or
at endpoints of the interval.
Answer: Extreme Value Theorem
7. If f is continuous on [a,b] and k is a number between f(a) and f(b), then there
exists at least one number c such that f(c)=k
Answer: Intermediate Value Theorem
8. If f(x) is continuous on the closed interval [a, b], differentiable on (a, b), and
satisfies f(a) = f(b), then for some c in the interval (a, b), we have f'(c) = 0 Answer:
Rolle's Theorem
9. Find HA: y = (x+2)/(sqrt(x^2+3))
Answer: y= +1 and y = -1
10.A pair of equations that define the x and y coordinates of a point in terms of a
1. If (c, f(c)) is a point of inflection of the graph of f, then either f"(c)=0 or f"
is undefined at c
Answer: Points of Inflection
2. Where first derivative is 0 or undefined
Answer: Critical Value
3. Use critical values and END POINTS in the function
Answer: Find absolute extrema
4. If m>n: NO HA
If m=n: HA = co-eff of m/co-eff of n
If m<n: HA: y = 0
Answer: Horizontal Asymptote Rules
5. If f(x) is continuous on [a,b] and differentiable on (a,b), there is at least one
point (x=c) where f'(c)= F(b)-F(a)/b-a
Answer: Mean Value Theorem
6. If f is continuous on [a,b] then f has an absolute maximum and an absolute
minimum on [a,b]. The global extrema occurs at critical points in the interval or
at endpoints of the interval.
Answer: Extreme Value Theorem
7. If f is continuous on [a,b] and k is a number between f(a) and f(b), then there
exists at least one number c such that f(c)=k
Answer: Intermediate Value Theorem
8. If f(x) is continuous on the closed interval [a, b], differentiable on (a, b), and
satisfies f(a) = f(b), then for some c in the interval (a, b), we have f'(c) = 0 Answer:
Rolle's Theorem
9. Find HA: y = (x+2)/(sqrt(x^2+3))
Answer: y= +1 and y = -1
10.A pair of equations that define the x and y coordinates of a point in terms of a
