What are the solution(s) to the quadratic equation 40 - x2 = 0?
1 answer:
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Answer:
f(x) = -2x + 7, when x > 1
f(x) = 4x + 1 when x ≤ 1
Step-by-step explanation:
The right side graph passe through points (1,5) and (2,3).
Hence, the equation of the line
⇒ (y - 5) = 2(1 - x)
⇒ y - 5 = 2 - 2x
⇒ y = -2x +7.......... (1)
Now, the left side graph passes through points (1,5) and (0,1)
Therefore, the equation of the graph will be
⇒ y - 5 = 4(x - 1)
⇒ y = 4x + 1 ........ (2)
Hence, the equation (1) gives the function in the right side of the given graph which does not include the point (1,5) and extends to the right from this point.
Therefore, f(x) = -2x + 7, when x > 1 (Answer)
Again, equation (2) gives the function in the left side of the given graph which includes the point (1,5) and extends to the left from this point.
Therefore, f(x) = 4x + 1 when x ≤ 1 (Answer)
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