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(c) Use average rates of change to approximate the in-stantaneous rate of change of f(x) at x = 2.5. (a) Make a table of values, rounded to two decimalplaces, for f(x) = log x (that is, log base 10) with=1, 1.5, 2, 2.5, 3. Then use this table to answerparts (b) and (c).(b) Find the average rate of change of f(x) between=1 and x 3.(c) Use average rates of change to approximate the in-stantaneous rate of change of f (x) at xx=1 and x = 3.2.6. If f(x) = x3 4x, estimate f' (3) using a table withvalues of x near 3, spaced by 0.001.7. Graph f(x)whether the derivative of f(x) at x = 3« is positiveor negative.13.sin x, and use the graph to decide8. For the function f(x) = log x, estimate f'(1). From thegraph of f(x), would you expect your estimate to begreater than or less than f'(1)?

Question

Please answer number 6.

(c) Use average rates of change to approximate the in-
stantaneous rate of change of f(x) at x = 2.
5. (a) Make a table of values, rounded to two decimal
places, for f(x) = log x (that is, log base 10) with
=1, 1.5, 2, 2.5, 3. Then use this table to answer
parts (b) and (c).
(b) Find the average rate of change of f(x) between
=1 and x 3.
(c) Use average rates of change to approximate the in-
stantaneous rate of change of f (x) at x
x=1 and x = 3.
2.
6. If f(x) = x3 4x, estimate f' (3) using a table with
values of x near 3, spaced by 0.001.
7. Graph f(x)
whether the derivative of f(x) at x = 3« is positive
or negative.
13.
sin x, and use the graph to decide
8. For the function f(x) = log x, estimate f'(1). From the
graph of f(x), would you expect your estimate to be
greater than or less than f'(1)?
help_outline

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(c) Use average rates of change to approximate the in- stantaneous rate of change of f(x) at x = 2. 5. (a) Make a table of values, rounded to two decimal places, for f(x) = log x (that is, log base 10) with =1, 1.5, 2, 2.5, 3. Then use this table to answer parts (b) and (c). (b) Find the average rate of change of f(x) between =1 and x 3. (c) Use average rates of change to approximate the in- stantaneous rate of change of f (x) at x x=1 and x = 3. 2. 6. If f(x) = x3 4x, estimate f' (3) using a table with values of x near 3, spaced by 0.001. 7. Graph f(x) whether the derivative of f(x) at x = 3« is positive or negative. 13. sin x, and use the graph to decide 8. For the function f(x) = log x, estimate f'(1). From the graph of f(x), would you expect your estimate to be greater than or less than f'(1)?

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check_circleAnswer
Step 1

f(x) = x3 + 4x

Hence, we can have the table for values of f(x) in the vicinity of x = 3 as shown on the white board.

f(x)
X
2.998
38.938
2.999
38.969
3.000
39.000
3.001
39.031
3.002
39.062
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f(x) X 2.998 38.938 2.999 38.969 3.000 39.000 3.001 39.031 3.002 39.062

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Step 2

Let\'s now define a = 3. Let\'s recall the formula for right hand derivative and left han...

f'(a) lima h) - f(a)
h
h-0
f'(a) = lima-h)- f(a)
-h
h-0
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f'(a) lima h) - f(a) h h-0 f'(a) = lima-h)- f(a) -h h-0

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Tagged in

Math

Calculus

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