A function is a relationship between two quantities, called the ___ and the ___?
1 answer:
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Answer:
The local maximum and minimum values are:
Local maximum
Local minima
Step-by-step explanation:
Let be . The determination of maxima and minima is done by using the First and Second Derivatives of the Function (First and Second Derivative Tests). First, the function can be rewritten algebraically as follows:
Then, first and second derivatives of the function are, respectively:
First derivative
Second derivative
Now, let equalize the first derivative to solve and solve the resulting equation:
The second-order polynomial is now transform into a product of binomials with the help of factorization methods or by General Quadratic Formula. That is:
The critical points are 0, 5.118 and -1.368.
Each critical point is evaluated at the second derivative expression:
x = 0
This value leads to a local maximum.
x = 5.118
This value leads to a local minimum.
x = -1.368
This value leads to a local minimum.
Therefore, the local maximum and minimum values are:
Local maximum
Local minima
(a) Differentiate each of the components to get r'(t). The rule is
.. d/dt (a*e^(bt)) = a*b*e^(bt)
The answer you have shown is the correct one.
(b) See the figure. The red curve is the position r(t) for 0 ≤ t ≤ 2. The dashed orange line is the tangent line, whose equation is
.. L(t) = r(0) +r'(0)*t = (2 +2t)i +(3 -3t)j
.. d/dt (a*e^(bt)) = a*b*e^(bt)
The answer you have shown is the correct one.
(b) See the figure. The red curve is the position r(t) for 0 ≤ t ≤ 2. The dashed orange line is the tangent line, whose equation is
.. L(t) = r(0) +r'(0)*t = (2 +2t)i +(3 -3t)j
Answer:
The left end approaches to + Infinite being an exponential function, and the right end to 0
Step-by-step explanation:
we have to remember the exponential function, the best way to find the answer is plotting the graph or arranging a table of values.
As you can see in the attached graph the y axis gets closer and closer to 0 as it moves forward in the x axis, and as it moves to the left the y axis starts increasing rapidly.
Also you got to keep in mind the way that functions behave in terms of the sign of its variable. for example the 10 in this equation only makes the curve to get wider, but if you change the sign to minus, the answer would be different.
