A asked in Science & MathematicsMathematics · 1 month ago

How do I find the points of the curve?

The question is 'at what points does the tangent to the curve, given by y=3 + x(to the power of 3) have a gradient of 12.

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  • 1 month ago
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    y = 3 + x³

    At what points is the slope of the tangent line equal to 12?

    The first derivative will give you a function of slopes of the original function.  Set that equal to 12 and then solve for the x's to find the x's of those points.  Then you can find the y's:

    dy/dx = 3x²

    12 = 3x²

    4 = x²

    ±2 = x

    There are 2 x's, so we find the 2 y's:

    y = 3 + (-2)³ and y = 3 + 2³

    y = 3 - 8 and y = 3 + 8

    y = -5 and 11

    So the two points are:

    (-2, -5) and (2, 11)

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