At what points on the given curve x = 4t3, y = 3 + 40t − 2t2 does the tangent line have slope 1?

ANSWER

The points are:

(32,-85)

and

EXPLANATION

The given parametric equation that defines the curve is:

We differentiate to get,

The slope of the tangent is given by;

For the slope to be 1, then we must solve the following equation for t.

When t=-2, we put -2 into the expression for x and y to get

x=4(-2)³ and y=3+40(-2)-2(-2)²

This implies that,

x=32, y=-85

Hence one point is (32,-85)

Similarly, when

Another point is

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