ESTIMATE THE DERIVATIVE OF A FUNCTION AT A GIVEN POINT FROM TABLE

To estimate the derivative of a function at a given point from table, we have to follow the steps given below.

Step 1 :

Determine the slope between point and the point directly to the left of point .

Step 2 :

Determine the slope between point and the point directly to the right of point.

Use the tables to estimate the value of the derivative at the given point. Indicate units of measures.

Problem 1 :

 a.   f'(8) b.   f'(3.5)

Solution :

a. To find f'(8) :

Here 8 lies between 7 and 9.

(7, 807) and (9, 902)

f'(8) = 47.5 visitors/hours

b. To find f'(3.5) :

f'(3.5) = 119 visitors/hours

Problem 2 :

 a. f'(17) b. f'(24.5)

Solution :

a. To find f'(17) :

f'(17) = -1.667  ºC per cm

b. To find f'(24.5) :

f'(24.5) = -3.667  ºC per cm

Problem 3 :

 a. f'(1.5) b. f'(11)

Solution :

a. To find f'(1.5) :

f'(1.5) = 5 students/year2

b. To find f'(11) :

f'(11) = -1.125 students/year2

Problem 4 :

 a. f'(47.5) b.  f'(9)

Solution :

a. To find f'(47.5) :

f'(47.5) = 3 pages per day

b. To find f'(9) :

f'(9) = -3.875 pages per day

Problem 5 :

 a. f'(20) b. f'(82.5)

Solution :

a. To find f'(20) :

f'(20) = -10.75 gallons/sec2

b. To find f'(82.5) :

f'(82.5) = -6.4285 gallons/sec2

Problem 6 :

 a. f'(25.5) b. f'(13.5)

Solution :

a. To find f'(25.5) :

f'(25.5) = 13.555 yards per carry

b. To find f'(13.5) :

f'(13.5) = -3 yards per carry

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