Question

(a) find the slope m of the tangent to the curve y = 5/ x at the point where x = a > 0.(b) find equations of the tangent lines at the points (1, 5) and 4, 5 2 .

Answer 1

(a) the slope of curve is calculated from the derivative of the curve expression y=5/x. In this problem, the slope m=-5/(a^2). (b) x=1, y=5，and m=-5, the tangent line is y-5=-5*(x-1). x=4, y=5/4, and m=-5/16, the tangent line is y-5/4=-5/16*(x-4)