Question

Use a system of equations to find the cubic function

f(x) = ax^{3} + bx^{2} + cx + d

that satisfies the equations. Solve the system using matrices.

f(−1) = 10

f(1) = 8

f(2) = 34

f(3) = 94

Answer #1

Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local
maximum value of 4 at x = −2 and a local minimum value of 0 at x =
1.

Find a cubic function
y = ax3 +
bx2 + cx +
d
whose graph has horizontal tangents at the points (-2, 8) and
(2, 2).

Use a system of linear equations to find the quadratic
function
f(x) = ax2 + bx + c
that satisfies the given conditions. Solve the system using
matrices.
f(1) = 3, f(2) = 12, f(3) = 25
f(x) =

For the function f(x)=ax3+bx2-5x+9,
determine the values of a and b so that f(-1)=12 and f'(-1)=3

. For the quartic function f(x) = ax4 + bx2 + cx + d, find the
values of a, b, c, d such that there is a local maximum at (0, -6)
and a local minimum at (1, -8). How do you find this?

The cubic polynomial P(x) = x3 + bx2 + cx + d (where b, c, d are
real numbers) has three real zeros: -1, α and -α.
(a) Find the value of b
(b) Find the value of c – d

. Find a cubic function f(x) with roots x = 4, x = 1, x = −2 and
f(1) = 16.
3. Sketch the graph of f(x) = (x − 2)/x^2−3x−4 showing zeros,
intercepts, and asymptotes.
4. Assume that world population(in billions of people) in t
years since 2016 is given by y = 7.7e^0.01t . When will the
population reach 9 billion?
5. Solve for x: log3 (x + 2) + log3 (x − 4) = 3.
6. Show...

A small aircraft starts its descent from an altitude of h = 4 3
mile, 4 miles west of the runway (see figure). (a) Find the cubic
f(x) = ax3 + bx2 + cx + d on the interval [−4, 0] that describes a
smooth glide path for the landing. f(x) = (b) The function in part
(a) models the glide path of the plane. When would the plane be
descending at the greatest rate? x =

1) find a cubic polynomial with only one root
f(x)=ax^3+bx^2+cx +d such that it had a two cycle using Newton’s
method where N(0)=2 and N(2)=0
2) the function G(x)=x^2+k for k>0 must ha e a two cycle
for Newton’s method (why)? Find the two cycle

Given that f(x) is a cubic function with zeros at −7 and −4i−1 ,
find an equation for f(x) given that ?(1)=8.

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