Question

Consider the function f(x)=arctan((x+5)/(x+4))

What is the slope of the tangent line at the inflection point? The
inflection point I got was: (-9/2, -pi/4).

If you could provide a sketch of the graph as well I'll give a thumbs up, thank you!

Answer #1

Let f(x)=22−x2f(x)=22-x2
The slope of the tangent line to the graph of f(x) at the point
(−4,6) is .
The equation of the tangent line to the graph of f(x) at (-4,6) is
y=mx+b for
m=
and
b=
Hint: the slope is given by the derivative at x=−4

Find the slope of the line tangent to the function sin(2x)+ x at
x = pi/4

2. The function f(x) = 1 1 + 1.25x 2 has one inflection point on
the interval 0 ≤ x ≤ 2.
(a) Find the inflection point of the function f(x). Write the
answer with ALL the decimal places the calculator gives. Do not
round the calculator answer. calculator answer:
(b)Sketch the graph of f(x) over the interval 0 ≤ x ≤ 2. Label
the inflection point of f(x) in your sketch. Give the window you
use.
(c)(2 points) Use...

. Find the slope of the tangent line to f-1 at the
point P(-1, 0) if f(x) = x+1/ x-1, and then find the
slope-intercept equation of the tangent line to the graph of
f-1 at P.

Find the linearization of the function f (x y) =
arctan (y / x) at point (1,1) and the tangent plane at that
point.

Being f (x) = x^2 - 4x - 3, determine the slope of the line
tangent to the curve of
f (x) at the point where x =3.
VIII. Being f (x) = 5x^2 + 3x - 9, determine the slope of the
line tangent to the curve of
f (x) at the point where x = -1.
IX. Determine the equation of the line to the curve of f (x) =
x^2 - 9x , at the point where...

Find the equation of the tangent line to the graph of the
function f(x)=(x^2+8)(x−2) at the point (1,−9).
I thought it was re-writen as (2x^2 + 8)(x-2) then plugging in 1
for x and solving. I came up withit in slope form y = -20x - 1 but
says im wrong. What steps did i miss?

Find the equation of the tangent line to the function
f(x)=8√(x)−6 at the point (64,58). Provide your answer in
slope–intercept form of a linear equation, y=mx+b, where m is the
slope and b is the y-intercept. Express m and b as exact
numbers.

Consider the function f(x) = √x and
the point P(4,2) on the graph f.
a)Graph f and the secant lines passing through the
point P(4, 2) and Q(x,
f(x)) for x-values of 3, 5, and 8.
b) Find the slope of each secant line. (Round your answers to
three decimal places.)
(line passing through Q(3, f(x)))
(line passing through Q(5, f(x)))
(line passing through Q(8, f(x)))
c)Use the results of part (b) to estimate the slope of the
tangent line...

1)Consider the function f(x)f(x) whose second derivative is
f″(x)=9x+8sin(x). If f(0)=4 and f′(0)=2, what is f(5)?
2) Consider the function f(x)=(7/x^3)−(2/x^5).
Let F(x) be the antiderivative of f(x) with F(1)=0.
3)Given that the graph of f(x) passes through the point (5,4)
and that the slope of its tangent line at (x,f(x)) is 3x+3, what
is f(2)?
Then F(2) equals

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