Answer:
For f(x) to be differentiable at 2, k = 5.
Step-by-step explanation:
For f(x) to be differentiable at x = 2, f(x) has to be continuous at 2.
For f(x) to be continuous at 2, the limit of f(2 – h) = f(2) = f(2 + h) as h tends to 0.
Now,
f(2 – h) = 2(2 – h) + 1 = 4 – 2h + 1 = 5 – 2h.
As h tends to 0, lim (5 – 2h) = 5
Also
f(2 + h) = 3(2 + h) – 1 = 6 + 3h – 1 = 5 + 3h
As h tends to 0, lim (5 + 3h) = 5.
So, for f(2) to be continuous k = 5
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<u>Given Function is</u>
- f ( x ) = 7x - 7 ------- eqn ( 1 )
<u>Now , put the value of x = 8 in eqn ( 1 )</u>
- f ( 8 ) = 7 ( 8 ) - 7
- f ( 8 ) = 56 - 7
- f ( 8 ) = 49 ------- eqn ( 2 )
<u>Now , put the value of x = 4 in eqn ( 1 )</u>
- f ( 4 ) = 7 ( 4 ) - 7
- f ( 4 ) = 28 - 7
- f ( 4 ) = 21 ------- eqn ( 3 )
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<u>From eqn ( 2 ) nd eqn ( 3 ) we get,</u>
- f ( 8 ) + f ( 4 )
- 49 + 21
- 70
Hope Helps! :)
C- 5 less than 6 times some number.
5 - 6t
42 divided by 5 is actually 8.4 however u cant have .4 of a rock so the answer is that each friend gets 8 rocks( including him)
