Question

1. Let f(x)=(x^2+1)(2x-3)

Find the equation of the line tangent to the graph of f(x) at x=3.

Find the value(s) of x where the tangent line is horizontal.

2. The total sales S of a video game t months after being introduced is given by the function

S(t)=(5e^x)/(2+e^x )

Find S(10) and S'(10). What do these values represent in terms of sales?

Use these results to estimate the total sales at t=11 months after the games release.

Answer #1

Let
fx=x2+12x-3
Find the equation of the line tangent to the graph of
f(x) at x=3
Find the value(s) of x where the tangent line is
horizontal.
2.The total sales of a video game months after being introduced
is given by the function
St=5ex2+ex
Find
S(10) and S'(10). What do these values represent
in terms of sales?
Use these
results to estimate the total sales at t=11 months after
the games release.

f(x)=1/2x ln x^4, (-1,0)
a) find an equation of the tangent line to the graph of the
function at the indicated point.
b) Use a graphing utility to graph the function and its tangent
line at the point.

Find the derivative of f(x) - In(2x)
1. what point on the graph of f(x) at which the tangent line is
horizontal?
2. what point on the graph of f(x) at which the tangent is
vertical?
3. is there a point on the graph f(x) at which the tangent has a
slope 1?

let f(x) = sqrt x^4+4x+4.find the equation of the tangent line
to the graph of f −1(a) when a = 3

find a point of the graph of the function f(x) = e^2x such that
the tangent line to the graph at that point passes through the
origin. Use a graphing utility to graph f and the tangent line is
the same viewing window

Find an equation of the tangent line to the graph of
2x+5/(1-2x)^3 at the point (-1,1)

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?

f(x)=3x^4-7x^2+2x+1
Find the tangent line at x=2

Find an equation for the tangent line to the graph of the given
function (-2,-1)
f (x)= x^2 - 5

determine the equation of tangent line to the graph of
y=tan(1/2x)+xcot(2x+pi/4) at x=pi/2

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