Consider the following. f(x) = x(x2 - 10x + 30) g(x) = x2 (a) Use a graphing utility to graph the region bounded by the graphs of the functions.(b) ) Find the area of the region analytically (c) Use the integration capabilities of the graphing utility to verify your results.
consider the function f(x) = 1 +
x3 e-.3x
a. what is f'(x)
b. what is f''(x)
c. what are the critical points of f(x)
d. are the critical points a local min or local max or
neither?
e. find the inflection points
f. if we define f(x) to have the domain of [2,50] compute the
global extreme of f(x) on that interval
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...
If f and g are both differentiable functions. If h = f g, then h'(2) is: ___________________
Given the function: y=sin(4x)+e^-3x and dx/dt = 3 when x=0. Then dy/dt = ________________ when x=0.
Let f(x) = ln (√x). The value of c in the interval (1,e) for which f(x) satisfies the Mean Value Theorem (i.e f'(c)= f(e)-f(1) / e-1 ) is: _________________________
Suppose f(x) is a piecewise function: f(x) = 3x^2 -11x-4, if x ≤ 4 and f(x) =...
1. For the function f(x)=x2−36 evaluate f(x+h).
f(x+h)=
2. Let f(x)=3x+4,g(x)=9x+12, and h(x)= 9x^2+ 24x+16. evaluate
the following:
a. (fg)(3)=
b. (f/g) (2)=
c. (f/g) (0)=
d.(fh)(-1)=
3. Let f(x)=2x-1, g(x)=x-3, and h(x) =2x^2-7x+3. write a formula
for each of the following functions and then simplify
a. (fh) (x)=
b. (h/f) (x)=
c. (h/g) (x)=
4.Let f(x)=5−x and g(x)=x^3+3 find:
a. (f∘g)(0)=
b.(g∘f)(0)=
c. (f∘g)(x)=
d. (g∘f)(x)=
5. Let f(x)=x^2+5x and g(x)=4x+5 find:
a. (f∘g)(x)=
b. (g∘f)(x)=
c. (f∘g)(0)=
d....
Consider the following function.
g(x, y) =
e− 4x2 + 5y2
+ 24 x
(a)
Find the critical point of g.
If the critical point is (a, b) then enter
'a,b' (without the quotes) into the answer
box.
(b)
Using your critical point in (a), find the value of
D(a, b) from the Second Partials test
that is used to classify the critical point.
(c)
Use the Second Partials test to classify the critical point
from (a).