Question

Consider the function ?= (2? − 3)^3(−4?^2 + 1)^2

a. Find the derivative of ?. Factor final answer as much as
possible.

b. Find the equation of the tangent line to the curve at the point
(1,25)

Answer #1

3. Let ?(?) be the revenue in dollars from selling ? units. If
?(200) = 540 and ?′(200) = 17..
a. Verbally interpret ?(200)
b. Estimate the revenue generated from the production of 201
units.
c. If the cost in dollars to produce ?? units is given by ?(?)
= ?.??x , is it profitable to raise the production to
201 units? Explain in a sentence.
4. An online shopping website has determined that the number
of items orders they...

Let f(x)=3x2+10x+3.
a) Find the derivative of f(x) using the definition of the
derivative.
b) Find the equation of the tangent line at point x=−1

) Consider the function f(x,y)=−2x^2−y^2.
Find the the directional derivative of ff at the point (1,−3)(1,−3)
in the direction given by the angle θ=π/2.
Find the unit vector which describes the direction in which ff
is increasing most rapidly at (1,−3).

1)Consider the curve y = x + 1/x − 1 .
(a) Find y' .
(b) Use your answer to part (a) to find the points on the curve
y = x + 1/x − 1 where the tangent line is parallel to the line y =
− 1/2 x + 5
2) (a) Consider lim h→0 tan^2 (π/3 + h) − 3/h This limit
represents the derivative, f'(a), of some function f at some number
a. State such an...

16.
a. Find the directional derivative of f (x, y) = xy at P0 = (1,
2) in the direction of v = 〈3, 4〉.
b. Find the equation of the tangent plane to the level surface
xy2 + y3z4 = 2 at the point (1, 1, 1).
c. Determine all critical points of the function f(x,y)=y3
+3x2y−6x2 −6y2 +2.

4)
Consider the polar curve r=e2theta
a) Find the parametric equations x = f(θ), y =
g(θ) for this curve.
b) Find the slope of the line tangent to this curve when
θ=π.
6)
a)Suppose r(t) = < cos(3t), sin(3t),4t
>.
Find the equation of the tangent line to r(t)
at the point (-1, 0, 4pi).
b) Find a vector orthogonal to the plane through the points P
(1, 1, 1), Q(2, 0, 3), and R(1, 1, 2) and the...

Consider the curve given by the equation
sin(?−?)=2?+?sin(x−y)=2x+y. The equation defines ?y as a function
?(?)y(x) near (0,0)(0,0).
(a) Find the equation of the tangent line to this curve at the
point (0,0)(0,0).
(b) Find ?″(0)y″(0).

1) Consider the curve y = e^cos(x) .
(a) Find y'
(b) Use your answer to part (a) to find the equation of the
tangent line to y = e^cos(x) at x = π/2.
2)
3)Consider the curve y = x + 1/x − 1 .
(a) Find y' .
(b) Use your answer to part (a) to find the points on the curve
y = x + 1/x − 1 where the tangent line is parallel to the line...

Part 1) Find the derivative of the function
f(x)=e^((x^2)/(x^2+4))
Part 2) Find the derivative of the function
f(t)=(e(^t^2)+4t)^4
Part 3) Find the derivative of the function y=log6sqrt(8x+3)
Part 4)
The number x of stereo speakers a retail chain is willing to
sell per week at a price of pp dollars is given by
x=78sqrt(p+24) -390
Find the supply and instantaneous rate of change of supply when
the price is 75 dollars.
Supply = 386
Instantaneous rate of change of supply...

f(x) = (sin x)2(cos
x)5
a) Find the first derivative of your function in fully factored
form
b) Find the critical numbers over the domain
c) Find the exact slope of the tangent to your function at x=
4
d) Find the exact equation of the tangent to your function at x=
4 in slope y intercept form

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