Question

At what point on the graph of `y = (1/2)x^2 - (3/2)` is the tangent line parallel to the line 4x - 8y = 5?

Answer 1

`(1/2, -11/8)`

Explanation:

The slope of the given line is `1/2`.

The slope of the tangent to the given curve `y=(1/2)x^2-(3/2)`, at (x, y) on the curve, is #y'=(1/2)(2x)=x.

So, for the parallel tangent the slope `= x = 1/2`. The corresponding `y= (1/2)(1/2)^2-(3/2)=(1/8)-(3/2)=-(11/8)`.

Answer: `(1/2, -11/8)`.
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