9514 1404 393
Answer:
c = -3; d = 5
Step-by-step explanation:
The function is differentiable if it is continuous and the derivative is continuous.
This function will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
5(3^2) +c = 45 +c
From the right, the limit is ...
d(3^2) -3 = 9d -3
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The derivative will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
f'(x) = 10x
= 10(3) = 30
From the right, the limit is ...
f'(x) = 2dx
= 2d(3) = 6d
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This gives us a pair of simultaneous equations in 'c' and 'd':
45 +c = 9d -3
6d = 30
The latter tells us d = 5. Then the former tells us ...
45 +c = 9(5) -3 ⇒ c = -3
The function is differentiable if c = -3 and d = 5.
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<em>Additional comment</em>
With these values, the function becomes ...

Answer:
Natalie is 13 years old, while Fred is 28 years old.
Step-by-step explanation:
Given that if you add Natalie’s age and Fred’s age, the result is 41, and if you add Fred’s age to 3 times Natalie’s age, the result is 67, to find how old Fred and Natalie are, the following calculation must be performed:
N + F = 41
3N + F = 67
(67 - 41) / 2 = N
26/2 = N
13 = N
13 x 3 + F = 67
39 + F = 67
F = 67 - 39
F = 28
28 + 13 = 41
Therefore, Natalie is 13 years old, while Fred is 28 years old.
X+6 of that is one of the answer options
Answer:
the "acceleration" is -15m/s (it's negative because it is slowing down, not speeding up[it might just be a positive 15m/s if it is called deceleration and not acceleration])
Step-by-step explanation:
30m/s (starting speed)/2 (the number of seconds it took to stop from 30m/s