The line is parallel to tangents drawn to the curve

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

The line 2y=8x+52y=8x+5 is parallel to tangents drawn to the curve y=x4−4x2+1y=x^{4}-4x^{2}+1. Determine all xx-coordinates where such tangents occur. (a) x=−1,  −1+52,  −1−52x=-1,\;\dfrac{-1+\sqrt5}{2},\;\dfrac{-1-\sqrt5}{2} (b) x=1,  −1,  2x=1,\;-1,\;2 (c) x=−1,  1+52,  1−52x=-1,\;\dfrac{1+\sqrt5}{2},\;\dfrac{1-\sqrt5}{2} (d) x=−1,  5,  −5x=-1,\;\sqrt5,\;-\sqrt5

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