BUSINESS CALCULUS TEST 1 EXAM
QUESTIONS WITH CORRECT ANSWERS
difference quotient represents (is equal to) - ANSWER-the slope of the secant line
passing through (x, f(x)) and (x+h,(f(x+h))
when do we use the difference quotient equation? - ANSWER-if we are looking for the
ARC between two points on a graph
it is preferable to simplify a difference quotient algebraically before - ANSWER-
evaluating it for particular values of x and h
what does h represent in the quotient equation? - ANSWER-the horizontal difference
between the two x values
conditions for a limit to exist
lim f(x) x-> a exists if: - ANSWER-it ONLY exists if
lim f(x) x-> a⁻ = lim f(x) x -> a⁺
Average Rate of Change - ANSWER-y₂ - y₁
----- where x₂≠x₁
x₂ - x₁
Instantaneous Rate of Change - ANSWER-slopes of tangent lines
derivative of a constant times a function
[c•f(x)]' - ANSWER-constant × derivative of that function
c • f(x)'
sum rule - ANSWER-derivative of a sum is the sum of the derivatives
[f(x) + g(x)]' = f(x)' + g(x)'
difference rule - ANSWER-[f(x) - g(x)]' = f(x)' - g(x)'
what does it mean for a line to be tangent? - ANSWER-it touches the edge of a curve
slopes of tangent lines are also known as - ANSWER-the instantaneous rate of change
the slope of the tangent line at (x,f(x)) is - ANSWER-m = lim h-> f(x+h) - f(x)
------------------
h
Three Steps in calculating a derivative - ANSWER-1. Write the difference quotient
2. simplify the difference quotient
QUESTIONS WITH CORRECT ANSWERS
difference quotient represents (is equal to) - ANSWER-the slope of the secant line
passing through (x, f(x)) and (x+h,(f(x+h))
when do we use the difference quotient equation? - ANSWER-if we are looking for the
ARC between two points on a graph
it is preferable to simplify a difference quotient algebraically before - ANSWER-
evaluating it for particular values of x and h
what does h represent in the quotient equation? - ANSWER-the horizontal difference
between the two x values
conditions for a limit to exist
lim f(x) x-> a exists if: - ANSWER-it ONLY exists if
lim f(x) x-> a⁻ = lim f(x) x -> a⁺
Average Rate of Change - ANSWER-y₂ - y₁
----- where x₂≠x₁
x₂ - x₁
Instantaneous Rate of Change - ANSWER-slopes of tangent lines
derivative of a constant times a function
[c•f(x)]' - ANSWER-constant × derivative of that function
c • f(x)'
sum rule - ANSWER-derivative of a sum is the sum of the derivatives
[f(x) + g(x)]' = f(x)' + g(x)'
difference rule - ANSWER-[f(x) - g(x)]' = f(x)' - g(x)'
what does it mean for a line to be tangent? - ANSWER-it touches the edge of a curve
slopes of tangent lines are also known as - ANSWER-the instantaneous rate of change
the slope of the tangent line at (x,f(x)) is - ANSWER-m = lim h-> f(x+h) - f(x)
------------------
h
Three Steps in calculating a derivative - ANSWER-1. Write the difference quotient
2. simplify the difference quotient
