The curve y= 1/3 x⁴ - 4x² -3x has a gradient of -3 at three points. Find the coordinates of these points.

Step-by-step explanation:

Step 1: Take the derivative of the function with respect to x

Now, you have the gradient of every point given the x value. We want the gradient to be -3, so,

Step 2: Set the derivative of the function equal to -3 and solve for x

We can see that one solution is x=0.

The other 2 solutions are:

Now that we found out the x value, we can plug it in back to the equation to find their respective y value:

x=0: y=0

x=sqrt(6): y=-12-3sqrt(6)

x=-sqrt(6): y=-12+3sqrt(6)

Hence we have our answer.

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step-by-step explanation: