For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the
following, and use it to graph the function.
Find: a)(2pts) Domain
b)(2pts) Intercepts
c)(2pts) Symmetry
d) (2pts) Asymptotes
e)(4pts) Intervals of Increase or decrease
f) (2pts) Local maximum and local minimum values
g)(4pts) Concavity and Points of inflection and
h)(2pts) Sketch the curve
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).
Find the derivatives of each of the following functions:
1. f(x) = (3x^2 + 2x − 7)^5 (2x + 1)^8
2. g(t) = cos(e^2x2+8x−3)
3. h(x) = e^x2/tan(2x−3)
4. Find dy/dx if cos(xy) = x^2y^5
Consider the function f(x)=(2x−1)e^−6x. Determine the critical
point(s) of f and locate all local extrema, then select all of the
following that are true of f.
Select all that apply:
f has a local maximum at x=1/3.
f has a local maximum at x=2/3.
f has a local minimum at x=1/3.
f has a local minimum at x=2/3.
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...
f(x)= 1/3x^3 + 5/2x^2 - 6x + 4; [-9,3]
The absolute maximum value is ____ at x = ___
(Use comma to separate answers as needed. Round to two
decimal places as needed)
The absolute minimum value is ____ at x = ___
(Use comma to separate answers as needed. Round to two
decimal places as needed)
Let f(x)=(x^2+1)*(2x-3)
Find the equation of the line tangent to the graph of f(x) at
x=3.
Find the value(s) of x where the tangent line is horizontal.