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Gradient =If z = 3t^2 + 6t + 4, what is the gradient of a graph of z against t at t =...

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minnsy229 | Honors

Posted June 21, 2012 at 7:11 AM via web

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Gradient =

If z = 3t^2 + 6t + 4, what is the gradient of a graph of z against t at t = 2.

You should enter your answer as a number not in scientific notation.

 

Gradient =

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 21, 2012 at 11:57 AM (Answer #1)

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It is given that z = 3t^2 + 6t + 4. The gradient of the graph of z versus t at t = 2 is given by the value of `(dz)/(dt)` at t = 2.

`(dz)/(dt) = 6t + 6`

At t = 2, 6t + 6 = 12 + 6 = 18

The gradient of the graph of z versus t at t = 2 is 18

 

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biditism | Student, Undergraduate | Honors

Posted June 21, 2012 at 9:50 AM (Answer #2)

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for the gradient first find the derivative of z with respect to t.

The derivative of z with respect to t is 6t+6.

Noe for the point at t=2

the gradient is 6*2+6 =18

 

theus the gradient is 18

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted June 21, 2012 at 12:27 PM (Answer #3)

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You should remember that you may find the gradient of the function differentiating the function `z(t)`  with respect to t such that:

`(dz)/(dt) = (d(3t^2 + 6t + 4))/(dt)`

`(dz)/(dt) = 6t + 6`

You need to find the gradient of the function at t = 2, hence, you should substitute 2 for t in equation `(dz)/(dt) = 6t + 6`  such that:

`(dz)/(dt)|_(t=2) = 6*2 + 6`

`(dz)/(dt)|_(t=2) = 18`

Hence, evaluating the gradient of the given function at t=2 yields `(dz)/(dt)|_(t=2) = 18` .

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