If z=2t^3 -7t how do I calculate the gradient of a graph of z against t at t = 3?
I assume you mean slope by "gradient"
This is a calculus question
find the derivative of z, the plug in t=3
To calculate the gradient of a graph of z against t at a specific value of t, you need to find the derivative of the function with respect to t and then substitute the desired value of t into the derivative.
In your case, you have the function z = 2t^3 - 7t. To find the derivative of this function, you need to apply the power rule:
1. Take the exponent of t and multiply it by the coefficient in front of t.
2. Subtract 1 from the exponent.
Let's find the derivative of z with respect to t:
z' = d/dt (2t^3 - 7t)
= 6t^2 - 7
Now that we have the derivative, we can substitute t = 3 into the equation to find the gradient at that point:
z'(3) = 6(3)^2 - 7
= 6(9) - 7
= 54 - 7
= 47
Therefore, the gradient of the graph of z against t at t = 3 is 47.