APPLIED CALCULUS FINAL EXAM
QUESTIONS AND ANSWERS
if f(x)=k, what is f1(x) - ANSWER-0
if f(x)=mx+b, what is f1(x) - ANSWER-m
if f(x)=x^n, what is f1(x) - ANSWER-nx^(n-1)
what does f1(x) of (a^x) equal - ANSWER-Ln (a) a^x
what does f1(x) of (Ln(x)) equal - ANSWER-1/x
what does f1(x) of e^(kx) equal - ANSWER-ke^(kx)
what does (f(g(x)))1 equal - ANSWER-f1(g(x))* g1(x)
what does (fg)1 equal - ANSWER-f1g+g1f
what does (f/g)1 equal - ANSWER-(gf1-fg1)/g^2
what is the point where f1(p)=0 or is undefined - ANSWER-critical point
f has a local ____ at p if f(p) is less than or equal to all values of f at points near p -
ANSWER-min
f has a local _____ at p if f(p) is greater than or equal to all values of f at points near p -
ANSWER-max
if f1(p) changes from negative to positive at x=p, then f has a local - ANSWER-min
if f1(p) changes from positive to negative at x=p, then f has a local - ANSWER-max
given a critical point:
if f11(p)>0 then f has a local - ANSWER-min
given a critical point:
if f11(p)<0 then f has a local - ANSWER-max
given a critical point:
if f11(p)=0 then - ANSWER-test is inconclusive
what point is where the graph of function f changes concavity - ANSWER-inflection
point
QUESTIONS AND ANSWERS
if f(x)=k, what is f1(x) - ANSWER-0
if f(x)=mx+b, what is f1(x) - ANSWER-m
if f(x)=x^n, what is f1(x) - ANSWER-nx^(n-1)
what does f1(x) of (a^x) equal - ANSWER-Ln (a) a^x
what does f1(x) of (Ln(x)) equal - ANSWER-1/x
what does f1(x) of e^(kx) equal - ANSWER-ke^(kx)
what does (f(g(x)))1 equal - ANSWER-f1(g(x))* g1(x)
what does (fg)1 equal - ANSWER-f1g+g1f
what does (f/g)1 equal - ANSWER-(gf1-fg1)/g^2
what is the point where f1(p)=0 or is undefined - ANSWER-critical point
f has a local ____ at p if f(p) is less than or equal to all values of f at points near p -
ANSWER-min
f has a local _____ at p if f(p) is greater than or equal to all values of f at points near p -
ANSWER-max
if f1(p) changes from negative to positive at x=p, then f has a local - ANSWER-min
if f1(p) changes from positive to negative at x=p, then f has a local - ANSWER-max
given a critical point:
if f11(p)>0 then f has a local - ANSWER-min
given a critical point:
if f11(p)<0 then f has a local - ANSWER-max
given a critical point:
if f11(p)=0 then - ANSWER-test is inconclusive
what point is where the graph of function f changes concavity - ANSWER-inflection
point
