# 14a) find the slope of the tangent to the curve a...

14a) find the slope of the tangent to the curve at the pont where.
14b. find the equations of the tangent lines at the pont (1,1)and (4, 1/2)

1. (a)
then
so the slope at the point where x = a is
(B)
solpe at the point (1,1) is = -1/2
so the equation of the tangent line is (y-1) =(-1/2)(x-1)
y = -x/2 +3/2
slope at the point (4,1/2) is = -1/16
then the equation of the tangent line at ( 4,1/2) is

(y-1/2)=(-1/16)(x-4)

y = -x/16+3/4
2. Quotient rule: (f/g)'=(gf'-fg')/g^2
The slope of the tangent line is the derivative of thefunction, so
f'(x)=y'=sqrt(x)*1'-1sqrt(x)'/sqrt(x)^2=-sqrt(x)/sqrt(x)^2,and install a for x, which doesn't mean anything until you get topart b, where you install the points (x,y) for their respectivevalues in the function.
3. 14 b
= x^(-1/2)
y' = -1/2*[x^(-1/3)......................1
Put x= 1 in eqn 1,
y ' = slope = -1/2
Equation of tangent => (y-y1)=m(x-x1)
Here m = -1/2 and x1,y1 = 1,1 Substitutethe valus and get the answers. Similarly you can do the otherone