Midterm Carolina

R.1-R.6

100

See page for question:

See page for answer: 

200

Find the Domain: 

Square root of: (7+2x)

What is [-7/2, infinity)

300

For f(x) = -4x²-x-1, find (f(x+h)-f(x))/h

What is (-8x-4h-1)?

400

Convert to radical notation. Assume all variables represent positive real numbers: 

(5m⁵+2)^-4/5

See answer on page

500

A function f is given by f(x) = 1/(x+3)². This function takes a number x, adds 3, squares the result, and takes the reciprocal of that result. 

FInd f(4), f(0), f(a), f(t+3), f(x+h), and f(x+h)-f(x)/h

f(4) = 1/49

f(0) = 1/9

f(a) = 1/(a+3)²

f(t+3) = 1/(t+6)²

f(x+h) = 1/(x+h+3)²

f(x+h)-f(x)/h = (-h-2x-6)/(x+3)²(x+h+3)²

1.1-1.3

100

See question on sheet:

The limit does not exist

200

Find limit: 

lim as x > 10 (x approaches 10)

(x²-100)/x-10

What is 20

300

Find the simplified difference quotient for the given function.

f(x)=4x⁴

What is:

16x³+24x²h+16xh²+4h³

400

See question on sheet: 

What is c = 2

500

Find the simplified difference quotient:

f(x) = square root (2x+7)

answer on paper

1.4-1.6

100

If f(x)=square root of (x) , find f'(11)

answer on page

200

Find derivative: 

y=-9.5x^1/5

Answer on sheet:

300

Find an equation for the tangent line to the graph of the given function at (-5,30)

f(x) = x²+5

What is y=-10x-20

400

Differentiate the function: 

y=(3x⁴-x+1)(-x⁵+7)

What is y'=-27x⁸+6x⁵-5x⁴+84x³-7

500

Question on page: 

Answer on page :) 

1.6-1.8

100

Find d²y/dx²

What is y=1/x³

200

Differentiate: 

g(x)=(9x-1)/(4x+9)+x³

What is g'(x)=85/(4x+9)²

300

Differentiate the function:

y=(4x²-13)^-14

What is y'=-112x(4x²-13)^-15

400

Differentiate the given function:

y=x² square root of (6x-1)

Answer on paper :) 

500

Find y'':

y=(3x+2)/(2x-5)

What is y''=(76)/(2x-5)³

2.1-2.3

100

Find the relative extreme points of the function, if they exist. Then sketch a graph of the function

G(x)=-x³+x²+8x+1

Relative min. point (-4/3, 149/27)

Relative max. point (2,13)

200

Find the relative extreme points of the function if they exist. Then sketch a graph of the function:

f(x)=x³-48x+123

Relative minimum point (4,-5)

Relative maximum point (-4,251)

300

Find the relative extreme points of the function, if they exist:

g(x)=square root of (x²+6x+45)

Relative maximum point (-3,6)

400

Draw a graph to match the description given:

f(x) is increasing over (-infinity,6) and decreasing over (6,infinity)

Answer on paper :) 

500

Find the relative extreme points of the function, if they exist. Then graph the function.

g(x)=6x³-4

There are no relative extremes