Question

calc help instantaneous rate of change

Answer 1

@Vocaloid

Answer 2

so they want you to use the derivative formula

[ f(x+h) - f(h) ] / h as h ---> 0

plug in the function and the x-value and you should be good to go

Answer 3

is c correct?

Answer 4

oh uh

I think they want you to plug in x = 6 so take the expression in C and plug that in

Answer 5

this one should be easier

Answer 6

oh that's easy just take the derivative of (1/2)t^2 -4t + 8 and plug in t = 10

Answer 7

50-40+8=18

Answer 8

you must take the derivative first

Answer 9

how do I take the derivative again

Answer 10

separate each term

(1/2)t^2 -4t + 8

(1/2)t^2

-4t

and

8

bring the exponent down as a product, reduce the original exponent by 1, and take the derivative of the base

(1/2)t^2 becomes

(1/2) * 2 * t^(2-1) * 1

Answer 11

repeat this process with -4t

Answer 12

as a reminder, the derivative of a single variable with exponent 1 is 1

so derivative of x is 1, derivative of a is 1, etc.

Answer 13

when taking the derivative, any coefficients like -4 just stay the same

so the derivative of t is just 1, because like I said, we have a single variable with exponent 1

so -4t ---> becomes -4*1 when you take the derivative

Answer 14

the derivative of a constant like 8 is just 0

Answer 15

so putting everything together:
the derivative of
(1/2)t^2 -4t + 8
becomes (1/2)(2)t - 4

now you can plug in t = 10

Answer 16

so -4 is still -4?

Answer 17

yes

Answer 18

so 6

Answer 19

yup

Answer 20

take the derivative of 4/x and plug in x = -1

that should give you the slope of the tangent

then see which of the choices has the same slope

Answer 21

remember you can re-write 4/x as 4x^(-1)

Answer 22

following our logic from before:

keep the coefficient

carry down the exponent as a new coefficient

then reduce the exponent by 1

Answer 23

4x^(-1)

becomes

4 * (-1) * x^(-2) as your derivative

plug in x = -1 and see what you get as the tangent slope.

Answer 24

4*-1=-4*1=-4

Answer 25

good so which choice has slope -4?

Answer 26

e

Answer 27

good so that's your sol'n

Answer 28

one more after this one

Answer 29

they give you the distance function and they want speed

so take the derivative of 0.8t^2 and plug in t = 1

Answer 30

would it be 0.8 ?

Answer 31

you have to bring the exponent down too

0.8t^2 ---> 0.8(2)t becomes the derivative

Answer 32

oh crap then it would be 1.6 I knew it was either 0.8 or 1.6

Answer 33

yup

Answer 34

last one I'm still unsure of this one someone helped me and told me it's c but I want to make sure

Answer 35

yeah I just did the calculations a while ago, D actually doesn't work mathematically so C is the only viable choice

Answer 36

ok just checking

Answer 37

ty

Answer 38

d actually was the answer

Answer 39

oh

yeah that makes sense they want you to plug in x = 6