If r(t) = 4e3t, 2e−3t, 4te3t , find t(0), r''(0), and r'(t) · r''(t).

we are given

Calculation of r(0):

we can plug t=0

Calculation of r'(0):

Firstly, we will find derivative

we can simplify it

now, we can plug t=0

Calculation of r''(0):

we can find second derivative

now, we can plug t=0

we get

Calculation of r'(0) · r''(0):

............Answer

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!