If z=2t^3 - 5t

what is the gradient of a graph ofzagainsttatt= 3?

The answerneeds to be a number not in scientific notation

Gradient = ???

Thanks

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- Jul 19th 2008, 09:30 AMstanton13Gradient Question
If z=2t^3 - 5t

what is the gradient of a graph of*z*against*t*at*t*= 3?

The answerneeds to be a number not in scientific notation

Gradient = ???

Thanks - Jul 19th 2008, 09:48 AMSimplicity
A cubic curve will have a range of gradients. To find the gradient at a specific point, find the derivative and insert the value at which you want to find the gradient (In this case when $\displaystyle t=3$).

$\displaystyle z=2t^3 - 5t \therefore \frac{\mathrm{d}z}{\mathrm{d}t} = 6t^2 - 5$.

Inserting $\displaystyle t=3$ into the derivative will give you the gradient at that point.