Problem 1
We'll use the product rule to say
h(x) = f(x)*g(x)
h ' (x) = f ' (x)*g(x) + f(x)*g ' (x)
Then plug in x = 2 and use the table to fill in the rest
h ' (x) = f ' (x)*g(x) + f(x)*g ' (x)
h ' (2) = f ' (2)*g(2) + f(2)*g ' (2)
h ' (2) = 2*3 + 2*4
h ' (2) = 6 + 8
h ' (2) = 14
<h3>Answer: 14</h3>
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Problem 2
Now we'll use the quotient rule
<h3>Answer: -2/9</h3>
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Problem 3
Use the chain rule
<h3>Answer: 12</h3>
Z-score for 30 = (30 - 25) / 5.8 = 0.8621
z-score for 20 = (20 - 25) / 5.8 = -0.8621
:
Note find probabilities from z-tables
:
Probability ( 20 < X < 30 ) = 0.8051 - 0.1949 = 0.6102
<h3>
Answer: C) x = 13</h3>
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Work Shown:
We have a right triangle with legs a = 5 and b = 12. The hypotenuse is c = x which is unknown for now.
Use the pythagorean theorem to find x.
a^2 + b^2 = c^2
5^2 + 12^2 = x^2
25 + 144 = x^2
169 = x^2
x^2 = 169
x = sqrt(169) .... apply the square root to both sides
x = 13
