Calculus I – Key Theorems, Rules, and Concepts Study Guide 2026/2027

CALCULUS I (MATH 1512 – 4 CREDITS)
UNIVERSITY OF NEW MEXICO EXAM
QUESTIONS AND ANSWERS 2026/2027 LATEST
UPDATE




1. 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




2. 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



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, 3. 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




4. 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




5. 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




6. Where first derivative is 0 or undefined

Answer: Critical Value



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