Find any stationary points in the function f(x) = 3x^2 + 2x

first differentiate the function f(X) = 3x² + 2x
1) The process of differentiation in this case involves bringing the current degree of power n on x down to be multiplied to the coefficient of the x variable with the power. Then you must change the degree of power on x by n-1, which is now the new power on the x.therefore : f^'(x) = 23x^2-1 + 12x^1-1 = 6x¹ + 2x⁰ = 6x + 2
2) The stationary point will satisfy the following equation f^'(X) = 0. Hence we must equate the differentiated equation to 0 and solve for any solutions.
Therefore: 6x+2 = 0. hence the solution is x = -2/6 = -1/3. (simplest form)
3) We have obtained the x value of the stationary point but we must also work out the y value to get a coordinate. So must input the x value obtained into f(x)
Therefore: f(-1/3) = 3*(-1/3)² + 2*(-1/3) = 3*(1/9) -(2/3) = 1/3 -(2/3) = -1/3