1. ## Derivatives

Suppose f has the values shown below:

f(1.9)=6.6, f(1.97)=6.905, f(2.0)=7, f(2.02)=7.059, f(2.2)= 7.5

Use the tabulated values of f to estimate.

1) f'(1.9)
The book says the answer to #1 is f'(1.9)= 4.357
2)f'(1.97)

Use the values f(1.9), f(1.95), f(2.0) and f(2.01) to estimate
(a) f'(1.9)
(b)f'(2.0)
(c)f'(2.01)

3) f(x)=x^2
the book says the answer for this one is
(a) -3.85
(b) 4.01
(c) 4.01

For both questions I do no understand how to get these answers. Am I suppose to use a formula? I would I go about solving these I do not understand derivatives well. Please explain I need to understand. Thank you.

2. Originally Posted by asweet1
Suppose f has the values shown below:

f(1.9)=6.6, f(1.97)=6.905, f(2.0)=7, f(2.02)=7.059, f(2.2)= 7.5

Use the tabulated values of f to estimate.

1) f'(1.9)
The book says the answer to #1 is f'(1.9)= 4.357
2)f'(1.97)

Use the values f(1.9), f(1.95), f(2.0) and f(2.01) to estimate
(a) f'(1.9)
(b)f'(2.0)
(c)f'(2.01)

3) f(x)=x^2
the book says the answer for this one is
(a) -3.85
(b) 4.01
(c) 4.01

For both questions I do no understand how to get these answers. Am I suppose to use a formula? I would I go about solving these I do not understand derivatives well. Please explain I need to understand. Thank you.
You are asked to use the slope of the secant (= the slope of the straight line between 2 points) as an approximate value of the slope of the tangent (=f'(x)):

You know 2 points: P(1.9, 6.6), Q(1.97, 6.905)

then the slope of the line PQ is:

$m_{PQ}=\dfrac{6.905 - 6.6}{1.97 - 1.9}=\dfrac{0.305}{0.07} \approx 4.32857...$

The other questions have to be solved in quite the same way.