Mohon bantuannya no. 17 matematika UTUL UGM Garis singgung kurva y = 15 (x-1/ x+k) di titik (x0,y0) dengan x0 = k+1 memotong sumbu-X di (1/2,0). Nilai y0 =... U

[tex]\displaystyle m=y'\\m=15\frac{x+k-(x-1)}{(x+k)^2}\\m=15\frac{x+k-x+1}{(x+k)^2}\\m=15\frac{k+1}{(k+1+k)^2}\\m=\frac{15k+15}{(2k+1)^2}\\\\y=mx+c\\0=\frac{15k+15}{(2k+1)^2}\cdot\frac12+c\\0=\frac{15k+15}{(2k+1)^2}+2c\\-2c=\frac{15k+15}{(2k+1)^2}\\c=-\frac{15k+15}{2(2k+1)^2}[/tex]

[tex]\displaystyle y_0=mx_0+c\\\frac{15k}{2k+1}=\frac{15k+15}{(2k+1)^2}(k+1)-\frac{15k+15}{2(2k+1)^2}\\k=\frac{k+1}{2k+1}(k+1)-\frac{k+1}{2(2k+1)}\\2k(2k+1)=2(k+1)(k+1)-k-1\\4k^2+2k=2k^2+4k+2-k-1\\2k^2-k-1=0\\(2k+1)(k-1)=0\\k=-\frac12\vee k=1\\\\y=\frac{15\cdot1}{2(1)+1}\\y=\frac{15}{2+1}\\\boxed{\boxed{y=5}}[/tex]