Consider the function and the value of a.
f(x) =
−2
x − 1
, a = 9. (a) Use mtan = lim h→0
f(a + h) − f(a)
h
to find the slope of the tangent line mtan =
f '(a).
mtan =
(b)Find the equation of the tangent line to f at x =
a.
(Let x be the independent variable and y be
the dependent variable.)
Consider the function. f(x) = x^2 − 1, x ≥ 1
(a) Find the inverse function of f.
f ^−1(x) =
(b) Graph f and f ^−1 on the same set of coordinate axes.
(c) Describe the relationship between the graphs. The graphs of
f and f^−1 are reflections of each other across the line ____answer
here___________.
(d) State the domain and range of f and f^−1. (Enter your
answers using interval notation.)
Domain of f
Range of f
Domain...
Consider the following function. f(x) = x^2 − 49 / x − 7 Find
each value. (If an answer does not exist, enter DNE.)
f(−7) = _____
lim x→−7 f(x) = _______
Determine whether the function is continuous or discontinuous at
x = −7. Examine the three conditions in the definition of
continuity.
5. Consider the function f(x) = -x^3 + 2x^2 + 2.
(a) Find the domain of the function and all its x and y
intercepts.
(b) Is the function even or odd or neither?
(c) Find the critical points, all local extreme values of f, and
the intervals on which f is increasing or decreasing.
(d) Find the intervals where f is concave up or concave down and
all inflection points.
(e) Use the information you have found to sketch...
Consider the following functions. f(x) = x − 3, g(x) = |x +
3|
Find (f ∘ g)(x).
Find the domain of (f ∘ g)(x). (Enter your answer using interval
notation.)
Find (g ∘ f)(x).
Find the domain of (g ∘ f)(x). (Enter your answer using interval
notation.)
Find (f ∘ f)(x).
Find the domain of (f ∘ f)(x). (Enter your answer using interval
notation.)
Find (g ∘ g)(x).
Find the domain of (g ∘ g)(x). (Enter your answer using...
Consider the function below.
f(x) =
ex
3 + ex
Find the interval(s) where the function is decreasing. (Enter
your answer using interval notation. If an answer does not exist,
enter DNE.)
Find the local maximum and minimum values. (If an answer does
not exist, enter DNE.)
Find the inflection point. (If an answer does not exist, enter
DNE.)
Consider the function below.
f(x) =
x2
x2 − 16
Find the interval(s) where the function is increasing. (Enter
your answer...
Consider the function f(x)= 1 + 1/x - 1/x2
Find the domain, the vertical and horizontal asymptotes,
the intervals of increase or decrease, the local minimum and
maximum values, the intervals of concavity and the inflection
points.
1.
Find the critical numbers of the function f (x) = x^3− 12x in the
interval [0, 3]. Then find the absolute maximum and the absolute
minimum of f(x) on the interval [0,3].
2. Using only the limit definition of derivative, find the
derivative of f(x) = x^2− 6x (do not use the formulas of
derivatives).