Question

f(x)=x^3- (3+2a^2)×^2+ (2+6a^2)×-4a^2

Define the function g(a): the smallest positive root of f(x)

Is the function g(a) continuous? Use a graph to justify ur answer

Answer #1

Define g(x) = f(x) + tan-1 (2x) on [−1, √3/2 ].
Suppose that both f'' and g'' are continuous for all x-values on
[−1, √3/2 ]. Suppose that the only local extrema that f has on the
interval [−1, √3/2 ] is a local minimum at x = 1/2 .
(a) Determine the open intervals of increasing and decreasing
for g on the interval [1/2 , √3/2] .
(b) Suppose f(1/2) = 0 and f(√3/2) = 2. Find the absolute...

Let f(x) = 2a^(2x) for some positive constant a. Express f(kx+2)
in terms of f(x) if k is a positive constant.
2) Determine the period, amplitude, phase shift and vertical
shift of y = 3 cos(2x - 2PI/5) + 1.5. Draw the graph over 2
cycles.
3) Draw the graph f(x) = (2x + 1)/(x^2 - 1)

4a). Let g be continuous at x = 0. Show that f(x) = xg(x) is
differentiable at x = 0 and f'(0) = g(0).
4b). Let f : (a,b) to R and p in (a,b). You may assume that f is
differentiable on (a,b) and f ' is continuous at p. Show that f'(p)
> 0 then there is delta > 0, such that f is strictly
increasing on D(p,delta). Conclude that on D(p,delta) the function
f has a differentiable...

Suppose that f is a differentiable function and define
g(x)=e^(2*f(x)+5x). Suppose that f(-2) = 1 and f ' (-2) = 2. Find g
' (-2).

Trigonometry – The cosine function
Determine all roots on ?=−8 ???(−6?−?/3)+1
Smallest positive root?
spacing between roots?
what ? ≤?≤?

1. Let f be the function defined by f(x) = x
2 on the positive real numbers. Find the
equation of the line tangent to the graph of f at the point (3,
9).
2. Graph the reflection of the graph of f and the line tangent to
the graph of f at the point
(3, 9) about the line y = x.
I really need help on number 2!!!! It's urgent!

Let f be the function defined by f(x)=cx−5x^2/2x^2+ax+b, where
a, b, and c are constants. The graph of f has a vertical asymptote
at x=1, and f has a removable discontinuity at x=−2.
(a) Show that a=2 and b=−4.
(b) Find the value of c. Justify your answer.
(c) To make f continuous at x=−2, f(−2) should be defined as
what value? Justify your answer.
(d) Write an equation for the horizontal asymptote to the graph
of f. Show the...

Prove that if f(x) is a continuous function and f(x) is not zero
then g(x) = 1/f(x) is a continuous function.
Use the epsilon-delta definition of continuity and please
overexplain and check your work before answering.

Define f: R (all positive real numbers) -> R (all positive
real numbers)
by f(x)= sqrt(x^3+2)
prove that f is bijective

Find the derivative of the function G(x)=1/2x^4+5x^3−x^2+6.8x+
square root of 3

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