Question

1.Determine the equation of the tangent to the curve at x=4

All = (3)!

2.Given the curve , find the equations to the tangents at x=5. Include in your solution a labeled sketch of the situation. (Yes, that said tangents! there is more than one solution to this problem!)

Personal advice: Think about Implicit differentiation and logarithmic differentiation. Only use Grade 12 Calculus knowledge.

Answer 1

lay= funerala ſa lara Sohntion: W. Giren: y = xx afley - ③ Af x= 4, y = 454 = 42=16. Now we shall find the stoße of the tangent line at X=4ie. at the point (4,16) to the coiffe: e givene " we shall find dy at 224. for this: dx & natirap logy soth sides y .. 16l lay I hun I luat some other A1234 le at (x,y) =(4,16); on these to an end 5) = 4424606). 4/27 (12²) = 4(2+2/02) = 8 (1+lez). so. &gr. of the tangent line attery (16) Y-16 = d y (x-4) =) Y-162 8(!+ ln2).(2-4) y 8 (1+ 2 x - 5 (1++ 18 8{1+1m 2} 2 + 16(1-2-3m2) 8 (1+ In 2)? - 16(1+2 lina). > 7 21 4d *) 4. Given the curve (x-232+ (y+1) 36. - 1x-:, (5-3)*+ ly+=367 4+144192 = 36 +19=27 = -! £35 So: xas, coresponds to two points on the curres Maway (18,-1+ 3v7) - 15 --36). How to find the tampent lines at there his posits to the quen wives you we shall find the slope of the tangent lines fint, 2-3 A 15,1438a). No - (-2) 71 2-5 33 from @ 12–3)2+4)*) - (944 >> 2(x-2)+2(y+) .-o. > -3 - 5 fan of first taupent live y-(-+3,3)-512-5) y +1-315 và 3 + 3 - 5 15% (14-3 A .--3-3): 2-S :: Gaqo op ho becomo tampout live ny +1+3w1 = (2-59 y+3+ 1 =4-5 x-v3y = 14+73 ]' And, 1+imwi 24539-44-05) 40 -vars (4.ti)