y=k question

Premium Tutorial

• Plot a graph of y=(x+5)/(x^2-x+6)
• Find stationary points: Say: k=(x+5)/(x^2-x+6), expand and factorize to kx^2+(-k-1)x+(6k-5)=0. Now use discriminant that must equal 0, so (-k-1)^2 - 4(k)(6k-5)=0 , -23k^2+22k+1=0 ; (k-1)(k+1/23) , k=1 or -1/23.
• Sub in y=1 and y=-1/23 to the function: 1=(x+5)/(x^2-x+6) , x^2-x+6=x+5 , x^2-2x+1=0, (x-1)(x-1)=0 , so x=1, therefore (1,1) is stationary point. -1/23=x+5/x^2-x+6, x^2+22x+121=0 , (x+11)(x+11), so x=-11, so (-11,-1/23) is stationary point.
• Find out as much as we can; SP's: (1,1) and (-11,-1/23) ; VA: none ; HA: y=0 ; y=0 - x=-5 ; x=0 - y=5/6 ; f(1000) = 0.0001 (a) ; f(-1000) = -0.0001 (b)
• With all this information, we can draw the graph which is on the next slide....

Slide 2