Todd owns 3 surfboards and 2 wet suits. If he takes one surfboard and one wetsuit
1 answer:
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Answer:
General Formulas and Concepts:
<u>Calculus</u>
Limits
Limit Rule [Variable Direct Substitution]:
L'Hopital's Rule
Differentiation
- Derivatives
- Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]:
Step-by-step explanation:
We are given the limit:
When we directly plug in <em>x</em> = 0, we see that we would have an indeterminate form:
This tells us we need to use L'Hoptial's Rule. Let's differentiate the limit:
Plugging in <em>x</em> = 0 again, we would get:
Since we reached another indeterminate form, let's apply L'Hoptial's Rule again:
Substitute in <em>x</em> = 0 once more:
And we have our final answer.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Answer:
Minimum at (-4, -10)
Step-by-step explanation:
x² + 8x + 6
The coefficient of x² is positive, so the parabola opens upward, and the vertex is a minimum.
Subtract the constant from each side
x² + 8x = -6
Square half the coefficient of x
(8/2)² = 4² = 16
Add it to each side of the equation
x² + 8x + 16 = 10
Write the left-hand side as the square of a binomial
(x + 4)² = 10
Subtract 10 from each side of the equation
(x+ 4)² -10 = 0
This is the vertex form of the parabola:
(x - h)² + k = 0,
where (h, k) is the vertex.
h = -4 and k = -10, so the vertex is at (-4, -10).
The Figure below shows your parabola with a minimum at (-4, -10).
