Question

Find the slope of tangent to the curve y=x-1/x-2 at x=10

Answer 1

Answer:

y=x-1/x-2 at x=10

y=x-1/x-2. x=2 at x=10

y=x-1/x-2. x=2

we know that slope of tangent is dy/dx

dy/dx=d(x-1/x-2)/dx

using quotient rule

as(u/v)1 =u1v-v1u/v2

dy/dx=(x-1)1 (x-2)-(x-2)1(x-1)/(x-2)2

dy/dx=1(x-2)-1(x-1)/(x-2)2

dy/dx=x-2-x+1/(x-2)2

so dy/dx=-1/(x-2)3

putting x=10

dy/dx=-1/(10-2)2

=-1/8(2)

=-1/64

hence 10 is =1/64