My Cal question

Question

Find an equation of the tangent line to the curve y = x ^4 + 1 that is parallel to the line y = 32x − 15

Answer 1

The slope of the tangent line to the graph of the function y(x) equals y'(x)=4x^3 and we need this to be equal to 32. Hence, we have that 4x^3=32 or x^3=8 or x=2. Thus, the tangent line will have an equation of the form y=32x+B. To find B we use that the line will pass through the point (2, 2^4+1=17) which gives that 17=64+B or B=-47. Therefore, we have the equation y=32x-47.