Question

Find a cubic function

* y* =

whose graph has horizontal tangents at the points (-2, 8) and (2, 2).

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.

Use a system of equations to find the cubic function
f(x) = ax3 + bx2 + cx + d
that satisfies the equations. Solve the system using
matrices.
f(−1) = 10
f(1) = 8
f(2) = 34
f(3) = 94

. 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 the formula for the cubic function (third degree
polynomial) whose graph has the given properties: • A y-intercept
of 63 and x-intercepts at x = −8, 25, 30.

curved etherical duty y=ax3 + bx2 + c + d with point (0,4) for him
and him with a tipping point; -1,2)the curve tangent at the tipping
point is equal to the x-axis, which is the value of a ,b, c,
d

find a function whose graph has the given asymptotes
x=-8, x=3, and y=8
a) f(x)= 8x^2 / x^2+5x-24
b) f(x)= 8x^2 / x^2-5x-24
c) f(x)= x^2+8 / x^2+5x-24
d) f(x)= x^2+8 / x^2-5x-24

Give an example of a rational function f whose graph has the
following properties.
vertical asymptote: x = 2
horizontal asymptote: y = 1
x-intercept: (5, 0)

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

For the function, find the point(s) on the graph at which the
tangent line is horizontal.
y=x^3-14x^2+9x+9
Select the correct choice below and if necessary, fill in the
answer box to complete your choice.
a. The point(s) at which the tangent line is horizontal
is(are___
b. The tangent line is horizontal at all points of the graph
c. There are no points on the graph where the tangent line is
horizontal.

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