Calc for Bio Exam Review

Product, Quotient and Chain Rules

100

Find the derivative of f(x)

f(x)=(x²+4)(3x-5)

f'(x)=9x²-10x+12

200

Find f'(1)

f(x)=(2x²+4)(3x+5)/4x-9

f'(x)=48x³-122x²-180x-188/(4x-9)²

f'(1)=-442/25

300

find f'(0)

f(x)=(x²-3)(x²-sqrt(5))

f'(x)=(x²-3)(2x)+(x²-sqrt(5))(2x)

f'(0)=0

400

find f'(x)

f(x)=-5(5x²+8)^-6

f'(x)=300x(5x²+8)^-7

500

find y'

y=x²+2/(9x-7)⁶

y'=-36x²-14x-108/(9x-7)⁷

Trig Stuff

100

A guy is standing 10 feet from a tree. He wants to know how tall the tree is. The angle from his feet to the top of the tree is 60 degrees. How tall is the tree?

Don't compute

Height of the tree = 10tan(60)

200

Convert 7pi/6 to degrees

210 degrees

300

y=5sin(3x)

find y'

y'=15cos(3x)

400

find f'(x)

f(x)=cos(4x²)+3x⁴

f'(x)=-8xsin(4x²)+12x³

500

find y'

y=cos(sin(e^2x))

y'=-2e^2xsin(sin(e^2x))cos(e^2x)

Deriv. of Log and Exponentials

100

y=ln(4x³)

find y'

y'=3/x

200

find f'(x)

f(x)=log₂(sin(x))

f'(x)=cot(x)/ln(2)

300

find f'(x)

f(x)=2e^{3x^2}

f'(x)=12xe^{3x^2}

400

find y'

y=x^3x

y=e^3xln(x)

y'=3x^3x(ln(x)+1)

500

find y'

y=7^xlog₇x

y'=(7^x/xln7)+(log₇x)(7^xln7)

Behavior of Graphs

100

Find all critical numbers of the function f(x).

f(x)=x⁴+12x³+36²+2

Critical numbers=-3,-6,0

200

For the following function, find the intervals where f(x) is increasing and decreasing.

f(x)=-5x-9

Decreasing on interval (-infinity,infinity)

Never increasing

300

Find the intervals where f(x) is increasing and decreasing.

f(x)=(x+9)/(x+4)

The function is decreasing on the interval               (-infinity,4), (-4,infinity)

400

Find the relative min and max of the function f(x).

f(x)=-x³-3x²+9x+5

min=(-3,-22)

max=(1,10)

500

Find the open intervals where the function f(x) is concave up and down.

f(x)=7/(x-7)

Up: (-infinity,7)

Down: (7,infinity)

Misc.

100

find the limit of y=x²-64/x-8 when x approaches 8

lim when x approaches 8 = 16

200

Find where f(x) is discontinuous. Where f(x) is discontinuous, find the limit when x approaches the value where f(x) is discontinuous.

f(x)=x²-81/x-9

discontinuous @ x=9

lim when x approaches 9 = 18

300

A culture contains 25,000 bacteria, with the population increasing exponentially. The culture contains 40,000 bacteria after 12 hours. Find the value for k in the exponential equation giving the number of bacteria after t hours.

hint: y=y_oe^kt

k=1/12ln(40000/25000)

400

For what values on the unit circle does cos(x)=0

x=pi/2 and 3pi/2

500

When and where is the exam tonight?

6:30-8pm W290 Chem Building