Using table to make conclusions about f'(x); limits

[badgersrule123]

A COUPLE QUESTIONS:

1.
Table:
x: 1.1 1.2 1.3 1.4
f(x): 4.18 4.38 4.56 4.73

Let f be a function that f ''(x) < 0 for all x in the closed interval [1,2]. Selected values of f are shown in the table above. Which of the following must be true about f ' (1.2)?

A. f ' (1.2) < 0
B. 0<f ' (1.2) < 1.6
C. 1.6 < f ' (1.2) < 1.8
D. 1.8 < f ' (1.2) < 2.0
E. f ' (1.2) > 2.0


2. What is the limit as h approaches zero of: {cos(3pie/2 + h) - cos(3pie/2)} divided by h?

A. 1
B. square root of two divided by 2
C. 0
D. -1
E. The limit does not exist.

 

[o_O]

Re: PLEASE HELP ME WITH CALCULUS!

1. Show us you're line of reasoning and we can help out wherever you're stuck.

2:
\(\displaystyle \lim_{h \to 0} \frac{cos(\frac{3\pi}{2} + h) - cos(\frac{3\pi}{2})}{h}\)

Two things you'll find useful:

\(\displaystyle cos(A+B) = cosAcosB - sinAsinB\)

\(\displaystyle \lim_{x \to 0} \frac{sinx}{x} = 1 \quad \mbox{Assuming you've gone over this ...}\)

This question is essentially saying what is the derivative of cosx at 3pi/2

 

[badgersrule123]

Re: PLEASE HELP ME WITH CALCULUS!

Do you just take like two numbers from the f(x) and subtract them and then divide that by two x numbers (subtracted).

Maybe like this:

4.56 - 4.18 divided by 1.3 - 1.1

????

 

[Deleted member 4993]

Re: PLEASE HELP ME WITH CALCULUS!

Do you just take like two numbers from the f(x) and subtract them and then divide that by two x numbers (subtracted).

Maybe like this:

4.56 - 4.18 divided by 1.3 - 1.1 ...yes but you have to look at it further than that

????

If you observe the numbers you can see f'(x) is increasing in the given domain.

so in addition approximate

\(\displaystyle f'_1(1.2) = \frac{(4.38-4.18)}{(1.2-1.1)}\)......................(1)

AND

\(\displaystyle f'_2(1.2) = \frac{(4.56 - 4.38)}{(1.3 - 1.2)}\)......................(2)

the actual f'(1.2) will be bounded by these two values