The point P( 0.5 , 10 ) lies on the curve y = 5 / x . Let Q be the point (x, 5 / x ) . a.) Find the slope of the secant line PQ for the following values of x. If x= 0.6, the slope of PQ is: If x= 0.51, the slope of PQ is: If x= 0.4, the slope of PQ is: If x= 0.49, the slope of PQ is: b.) Based on the above results, guess the slope of the tangent line to the curve at P(0.5 , 10 ).

Answer:Based on the results  it is expected that the slope of the tangent line at the point (0.5,10) is -20.Step-by-step explanation:To see that compute, the slopes for the given points as follows:1. For [tex]x=0.6[/tex] we have:[tex]m=\dfrac{(5/0.6)-10}{0.6-0.5}=-16.66[/tex]2. For [tex]x=0.51[/tex] we have:[tex]m=\dfrac{(5/0.51)-10}{0.51-0.5}=-19.60[/tex]3. For [tex]x=0.4[/tex] we have:[tex]m=\dfrac{(5/0.4)-10}{0.4-0.5}=-25.00[/tex]4. For [tex]x=0.49[/tex] we have:[tex]m=\dfrac{(5/0.49)-10}{0.49-0.5}=-20.40[/tex]So, we observe that the slope of the tangent line at [tex](0.5, 10)[/tex] is close to the value -20.The graph shown below is useful to see the secant lines that approximates the tangent line.