Gradient =

If *z* = 3*t*^2 + 6*t* + 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. **

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Gradient =

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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**

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**

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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