Question

Let f(x) be a quadratic function such that f(0)=−6 and ∫f(x)x2(x+5)7dx Determine the value of f′(0).

Answer #1

Consider the quadratic function f, given by f(x) = −x2 + 6x−8.
(i) Determine if the graph of y = −x2 + 6x − 8 is concave up or
concave down, providing a justiﬁcation with your answer. (ii)
Re-write the equation of the quadratic function f, given by f(x) =
−x2 +6x−8, in the standard form f(x) = a(x−h)2+k by completing the
square. Hence determine the vertex of the graph of y = f(x).
(iii) Identify the x-intercepts and y-intercept...

) Let
.f'(x)=x2-4x-5
Determine the interval(s) of x for which the function
is increasing, and the interval(s) for which the function is
decreasing.
Find the local extreme values of f(x) , specifying
whether each value is a local maximum value or a local minimum
value of f.
Graph a sketch of the graph with parts (a) and (b) labeled

A quadratic function is given:
f(x)=x2 + 4x − 2
a) express f in standard form (I already got that and it was
(x+2)^2-6
b) sketch a graph of f
c) Find the maximum or minimum value of f. Is this value a
maximum or minimum value?

Let f be the function given by f (x, y) = 4ay2
−x2y3 −x2 for all (x, y) in
R2, where
a ∈ R.
(a) Determine all stationary points to f when a = 0.
(b) Determine all stationary points to f when a > 0.
(c) Determine all stationary points to f when a < 0.
(d) Determine the Taylor polynomial of the second order for f
origin when a = −1.

Consider the Rosenbrock function, f(x) = 100(x2 -
x12)2 + (1
-x1)2. Let x*=(1,1), the minimum of the
function.
Let r(x) be the second order Taylor series for f(x) about the
base point x*, r(x) will be a quadratic, and therefore can be
written:
r(x) = A11(x1-x1*)2
+ 2A12(x1-x1*)(x2-x2*) +
A22(x2-x2*)2 +
b1(x1-x1*) +
b2(x2-x2*) + c
Find all the coefficients in the formula for r(x) - What is
A11, A12, A22, b1,
b2, and c?

Find the quadratic function that is the best fit for f(x)
defined by the table below. x 0 2 4 6 8 10 f(x) 0 401 1598 3602
6391 9990 The quadratic function is y equals = nothing . (Type an
equation using x as the variable. Round to two decimal places as
needed.)

Determine where the given function is increasing and where it is
decreasing.
f(x)=x4-2x2-9
f(x)=x2(6-x)2

Let f be a function for which the first
derivative is f ' (x) = 2x 2 - 5 / x2 for x
> 0, f(1) = 7 and f(5) = 11. Show work for all
question.
a). Show that f satisfies the hypotheses of the Mean
Value Theorem on [1, 5]
b)Find the value(s) of c on (1, 5) that satisfyies the
conclusion of the Mean Value Theorem.

1. Given the following quadratic function: f(x)=4x2-12x+5
a. Use the method of completing the square to rewrite the
equation of f
b. What are the coordinate of the vertex of f
c. What are the zeros of f (ker(f))
d. What is the image of f (image(f))
e. Describe the simple transformations that take x2 to f(x)

Let f(x) = x2/3 (2x − 5). Find the absolute maximum
value and the absolute minimum value of f on [0,8].

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