The particle's position as a funciton of time is given as `x=5t^2-9t+3`. Find out the maximum value of position co-ordinate? Also, plot the graph.

Explanation

To find the maximum value of the position coordinate given by the equation \( x = 5t^2 - 9t + 3 \), we will follow these steps:

### Step 1: Find the first derivative
We need to find the first derivative of the position function \( x \) with respect to time \( t \):
\[ \frac{dx}{dt} = \frac{d}{dt}(5t^2 - 9t + 3) \]
Using the power rule, we differentiate:
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