SI PASS MATH 155 Exam 2 Review!

Applications of Derivatives

100

Identify the critical point. f(x)= x²-6x

(3,-9)

200

For what values is the function increasing? f(x)= (1-x²)/x

the function is never increasing 

300

Identify the inflection point. f(x)= x³-3x²​​​​

(1,-2)

400

When is the function concave up? f(x)= 1-x³

when x<0 or (-infinity,0)

500

When is the function concave downward? f(x)= (x+1)/(x-1)

when x>1 or (1, infinity) 

Exponential Functions

100

Solve 2(e^3x-5)-7=9

x=ln(8)+5/3

200

Derive. f(x)= (e^-2x+3)²

-4(e^-2x+3)(e^-2x)

300

Derive. f(x)= (9e^x+1)/(3e^x+1)

6e^x/(3e^x+1)²

400

Find the equation to the tangent line at the curve of f(x)= e^{-x^2} at x=3

y= (-6/e⁹)x+ (19/e⁹)

500

Find the inflection poitn for the f(x)= xe^-x

x=0,1/2

LogFunctions

100

Write the expression as a single logarithm. ln(x)-1/2ln(x+2)-3ln(1-squ(x))

ln[x/squ(x+2)(1-squ(x))³]

200

Solve. log(x)+log(x-11)=log(12)

x=12

300

Derive. y=ln(squ(x+1/3x-4))

1/2[-4/(x+1)(3x-4)]

400

The equation of the tangent line to the graph y=xln(x) at x=1 

y=x-1

500

Derive. y=x²ln(e^2x-1)

2xln(e^2z-1)+(2x²e^2x/e^2x-1)

Word Problems

100

In the long run, f(x)= e^1-3x+4 will reach.... 

a. y=4

b. y= infinity

c. y=-inifinty

d. y=-4

y=4!

200

The equation of the tangent line to the curve of y=e^x-e^-x at its inflection point is? 

y=2x

300

The inflection point of the function of y=ln(1+x²) is... 

(1,ln(2))

400

How much interest is earned if $10,000 is initally depostied for 20 years at an interest rate of 8% compounded continuoulsy? 

A=10,000e^(0.08)(20)

500

Find the equation of the the tangent line(s) of e^{-x^2} at its inflection point. 

y=-2x+1 

y= (-1/e^1/4)x+ 3/2e^1/4