Question

1. Find a function f given that the slope of the tangent line to the graph of f at any point P(x, y) is given by y' = − 4xy x2 + 1 and the graph of f passes through the point (2, 1).

2. The world population at the beginning of 1980 (*t* =
0) was 4.5 billion. Assuming that the population continued to grow
at the rate of approximately 2%/year, find a function
*Q*(*t*) that expresses the world population (in
billions) as a function of time *t* (in years since
1980).

Q(t) = |

What will be the world population at the beginning of 2012? (Round
your answer to one decimal place.)

billion

Answer #1

find the point on the graph of the given function at which the
slope of the tangent line is the given slope.
f(x) = x^3+12x^2+56+15
slope of the tangent line = 8

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

. 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 equation of the line tangent to the graph of the given
function at the point with the indicated x-coordinate.
f(x) = (x0.5 + 8)(x2 + x); x = 1

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

1.) Find the equation of the tangent line to the graph of the
function f(x)=5x-4/2x+2 at the point where x=2
2.) Find the derivative: r(t)=(ln(t^3+1))^2

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 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 graph of the given
function at the given value of x:
f(x)= (x^2 +12)^3/4 where x=2. please show work .

Find an equation of the line that is tangent to the graph of
f and parallel to the given line.
Function
Line
f(x) = x2
6x − y + 9 = 0

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