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When a function can be written as the sum of two or more functions, the derivative can be found by adding together the derivatives of each of the component functions.

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The derivative of this function is the function itself.

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If a function can be written as the difference of two other functions, the derivative is found by writing the difference of the two individual functions.

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To find the derivative, multiply by the exponent of the variable and reduce the exponent by one.

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Use the reciprocal of the input variable as the derivative.

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When a function is multiplied by a constant, take the derivative of the function, then multiply by the constant.

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The derivative is always zero.

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Multiply the function by the natural logarithm of the base.

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Why is the derivative of a constant 0?

Let x ( t ) = t^ 3 ? 4 t^ 2 + 1

and y ( t ) = t^ 3 ? 5 t^ 2 + 2 t + 8

At t =1,

x(1)=x(1)=
y(1)=y(1)=

dx/dt | t=1 =
dy/dt | t=1 =

dy/dx | t=1 = tangent slope =

speed(1) =

Write a paragraph on a current national event.

Your paragraph should include at least 5-7 sentences. At least two sentences should be opinion statements and at least two sentences should be factual statements. Identify the opinion and factual sentences.

Let y = f (t) = t 2, where t is the time in seconds and y is the distance in meters that an object falls on a certain airless

a) Draw a graph of this function between t = 0 and t = 3. Make a table of the average speed of the falling object between the following intervals:

2 sec and 3 sec; 2 sec and 2.1 sec; 2 sec and 2.01 sec; 2 sec and 2.001 sec.

b) Use algebra to find a simple formula for the average speed between time 2 and time 2+∆t (∆t means the change in t or the difference between the two t values).

Hint: You will find the average speed just like you did in part a) but the endpoints of your interval will be (2, f(2)), and (2+∆t , f(2+∆t ))
Check: If you substitute ∆t = 1, 0.1, 0.01, 0.001 in this formula you should again get the answers to part a) since those were the changes in time over each of the intervals you used.

c) Using your formula for average speed (which should be in simplified form) determine what happens as ∆t approaches 0. This is the instantaneous speed.

d) On your graph of y = t 2 draw the straight line through the point (2, 4) whose slope is the instantaneous velocity you just computed; it should of course be the tangent to the curve at that point.

A train arrives at a station such that the time between arrivals has a rate of exponential distribution of 1/λ. In order to get home, you decide to wait for the train for t minutes. If the train arrives before t minutes, you take the train home which takes time X. If the train has not arrived after t minutes, you walk home which takes time Y. What is the expected total time from getting to the train stop until getting home?

write a paragraph on the following topic:

Locate a headline in a newspaper or online news web site. Identify two effects that might occur due to the headline.

Explain how you used the rules from the lesson in your paragraph. Your paragraph should contain 4-7 sentences.

La splendida sposa Sarah-Jane ha scelto Essense of Australia Style # D2512, un abito da sposa vintage glam. Caratterizzato da un ampio motivo in pizzo aperto, questo vestito inizia dalla scollatura e si estende fino all'orlo. Perle solide e testurizzate sono applicate al pizzo Gillne.it, che dona un aspetto glamour e deciso. La leggera scollatura a V sul corpetto di questo vestito è evidenziata da spalline sottili e un cinturino triplo, che si aggiungono al look di ispirazione vintage. La parte posteriore completamente aperta è evidenziata da un bordo di perline e da uno strascico in pizzo. "Volevo sembrare la migliore versione di me stessa nel mio grande giorno", ha detto Sarah-Jane.


La signora Hudson ha scelto l'abito più perfetto per il suo matrimonio “rustico e rilassato”. “Il nostro matrimonio si è svolto in un bellissimo vecchio fienile. I nostri centrotavola ci rispecchiavano come coppia; abbiamo usato bottiglie vuote di Jack Daniels e Coca - La bevanda preferita di Ben è Jack e io amo la Coca!

Help me please I beg you