MATH 201 Final Exam with verified answers
secant |line |slope |and |average |velocity |equation |- |verified |answers(f(c+h)-f(c))/h
tangent |line |slope |and |instantaneous |velocity |equation |- |verified |answersf'(c)=lim |h->0 |((f(c+h)-f(c))/h)
what |does |"h" |represent? |- |verified |answersdistance |between |2 |points
formula |for |average |velocity |on |an |interval |- |verified |answersAV[a,b]= |(s(b)-s(a))/(b-a)
formula |for |instantaneous |velocity |on |an |interval |- |verified |answersIV |@ |t=a |= |lim |b->a |((s(b)-s(a))/(b-
a))
what |does |the |original |function |represent? |- |verified |answersposition
what |to |the |first |derivative |represent? |- |verified |answersvelocity
what |does |the |second |derivative |represent? |- |verified |answersacceleration
what |does |f'(x) |> |0 |on |an |interval |say |about |the |original |function? |- |verified |answersit |says |that |f(x) |is
|increasing |on |the |interval
what |does |f'(x) |< |0 |on |an |interval |say |about |the |original |function? |- |verified |answersit |says |that |f(x) |is
|decreasing |on |the |interval
what |information |does |a |positive |f"(x) |give |us |about |f(x), |f'(x), |and |the |concavity? |- |verified |answersit |
says |that |f(x) |is |increasing, |f'(x) |is |increasing, |and |it |is |concave |up
what |information |does |a |constant |f"(x) |at |0 |give |us |about |f(x), |f'(x), |and |the |concavity? |- |verified |
answersit |says |that |f(x) |is |increasing, |f'(x) |is |constant, |and |that |there |is |no |curl
what |information |does |a |negative |f"(x) |give |us |about |f(x), |f'(x), |and |the |concavity? |- |verified |answersit
|says |that |f(x) |is |increasing, |f'(x) |is |decreasing, |and |it |is |concave |down
what |does |differentiable |mean? |- |verified |answerswhen |it |makes |sense |to |talk |about |something's |
derivative
what |are |3 |examples |of |non-differentiable |graphs/functions? |- |verified |answerscusps, |vertical |
tangents, |and |discontinuous |functions
what |does |a |limit |at |x=a |tell |us |about |the |function's |continuity |and |differentiability? |- |verified |
answersthat |f(x) |is |continuous |at |x=a |and |is |differentiable |at |x=a
what |does |non-differentiable |mean? |- |verified |answersthat |is |doesn't |make |sense |to |talk |about |how |
steep |the |function |is
what |is |a |"zero"? |- |verified |answersan |x-intercept
constant |rule |for |derivatives |- |verified |answersd/dx(c)= |0
secant |line |slope |and |average |velocity |equation |- |verified |answers(f(c+h)-f(c))/h
tangent |line |slope |and |instantaneous |velocity |equation |- |verified |answersf'(c)=lim |h->0 |((f(c+h)-f(c))/h)
what |does |"h" |represent? |- |verified |answersdistance |between |2 |points
formula |for |average |velocity |on |an |interval |- |verified |answersAV[a,b]= |(s(b)-s(a))/(b-a)
formula |for |instantaneous |velocity |on |an |interval |- |verified |answersIV |@ |t=a |= |lim |b->a |((s(b)-s(a))/(b-
a))
what |does |the |original |function |represent? |- |verified |answersposition
what |to |the |first |derivative |represent? |- |verified |answersvelocity
what |does |the |second |derivative |represent? |- |verified |answersacceleration
what |does |f'(x) |> |0 |on |an |interval |say |about |the |original |function? |- |verified |answersit |says |that |f(x) |is
|increasing |on |the |interval
what |does |f'(x) |< |0 |on |an |interval |say |about |the |original |function? |- |verified |answersit |says |that |f(x) |is
|decreasing |on |the |interval
what |information |does |a |positive |f"(x) |give |us |about |f(x), |f'(x), |and |the |concavity? |- |verified |answersit |
says |that |f(x) |is |increasing, |f'(x) |is |increasing, |and |it |is |concave |up
what |information |does |a |constant |f"(x) |at |0 |give |us |about |f(x), |f'(x), |and |the |concavity? |- |verified |
answersit |says |that |f(x) |is |increasing, |f'(x) |is |constant, |and |that |there |is |no |curl
what |information |does |a |negative |f"(x) |give |us |about |f(x), |f'(x), |and |the |concavity? |- |verified |answersit
|says |that |f(x) |is |increasing, |f'(x) |is |decreasing, |and |it |is |concave |down
what |does |differentiable |mean? |- |verified |answerswhen |it |makes |sense |to |talk |about |something's |
derivative
what |are |3 |examples |of |non-differentiable |graphs/functions? |- |verified |answerscusps, |vertical |
tangents, |and |discontinuous |functions
what |does |a |limit |at |x=a |tell |us |about |the |function's |continuity |and |differentiability? |- |verified |
answersthat |f(x) |is |continuous |at |x=a |and |is |differentiable |at |x=a
what |does |non-differentiable |mean? |- |verified |answersthat |is |doesn't |make |sense |to |talk |about |how |
steep |the |function |is
what |is |a |"zero"? |- |verified |answersan |x-intercept
constant |rule |for |derivatives |- |verified |answersd/dx(c)= |0
