Question

Consider the following. y = 6x^4 − 5x − 1/4 − x^2

A)Find the value of y when x = 1.

y(1) =

B Find dy/dx .

dy/dx =

C Find the exact value of dy/dx when x = 1.

dy/dx =

D Write the equation of the tangent line to the graph of y = 6x4 − 5x − 1 4 − x2 at x = 1. Check the reasonableness of your answer by graphing both the function and the tangent line.

Answer #1

Write the equation of the tangent line to the graph of y = (x^2
− 16x)/(4x − x^3) at x = 4. Check the reasonableness of your answer
by graphing both the function and the tangent line

y = x3 − 4x2 + 8
Evaluate y when
x = 1.
y(1) =
Find
y'.
y' =
Evaluate
y'
when
x = 1.
y'(1) =
Write the equation of the tangent line to the curve at
x = 1.
As a check, graph both the function and the tangent line.

Use implicit differentiation to find dy dx for x^2 y^3 + 3y^2 −
5x = −10.
(b) Find the equation of the line tangent to the curve in part
a) at the point (1, 2).

3. Consider the equation:
x^2y −√y = 2 + 4x^2
a) Find dy/dx using implicit differentiation. b)Construct the
equation of the tangent line to the graph of this equation at the
point (1, 9)

1). Consider the following function and point.
f(x) = x3 + x + 3; (−2,
−7)
(a) Find an equation of the tangent line to the graph of the
function at the given point.
y =
2) Consider the following function and point. See Example
10.
f(x) = (5x + 1)2; (0, 1)
(a) Find an equation of the tangent line to the graph of the
function at the given point.
y =

(A) Assume that x and y are functions of
t. If y = x3 + 6x and dx/dt = 5, find dy/dt
when x = 3.
dy
dt
= ?
(B) Assume that x and y are positive functions
of t. If x2 + y2 = 100 and dy/dt =
4, find dx/dt when y = 6.

Given the function g(x) = x^4 – 5x, find the slope of the curve
at the point (1,-4).
Also, find an equation for the line tangent to the graph at this
point.

Consider x^2 +sin(y)=4xy^2 +1
a.)Use Implicit differentiation to find dy/dx
b.) find an equation tangent of the line to the curve x^2
+sin(y)=4xy^2 +1 at (1,0)

1) Solve the given differential equation by separation of
variables.
exy
dy/dx = e−y +
e−6x −
y
2) Solve the given differential
equation by separation of variables.
y ln(x) dx/dy = (y+1/x)^2
3) Find an explicit solution of the given initial-value
problem.
dx/dt = 7(x2 + 1), x( π/4)= 1

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

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