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
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.