Lecture 12

Question 1

given a table of values representing g(x) and g’(x) and a graph represetning f(x), how do you compute the derivative of f[g(x)]|x=1?

Answer 1

1. write out the chain rule formula for the derivative
2. plug the x value into the formula
3. find the y value for g(1) because you have to work form the brackets first
4. use that answer to find the derivative of f using two points on the graph near the value of interest then use the slope formula to find the slope
5. Use the table to find g’(x)

Question 1

if the slope of f is always positive and the slope of g is always negative is for instance f[g(x)] increasing or decreasing?

Answer 1

1. write the chain rule formula of the function
2. add where the plus and minus will be in the formula
3. multiply the signed together to get the overall sign
4. determine whether the function is increasing or decreasing

Question 2

what do the sine and cosine functions have in common?

Answer 2

they both oscillate

Question 3

what is the formula to find the period? what do B mean?

Answer 3

2pi/B
B is the number beside t

Question 4

what rate does a linear function have?

Answer 4

constant rate

Question 5

how can you tell if a rate is defined?

Answer 5

1. find the derivative of the function
2. check for verticle and horizontal asymtotes

Question 6

when should you use the product rule?

Answer 6

when you have two different functions multiplied by each other

Question 7

what is the formula for the product rule?

Answer 7

y’=f’g+fg’