Find the slope m of the tangent to the curve y = 7/ x at the point where x = a > 0.

Question

(a) Find the slope m of the tangent to the curve y = 7/ x at the point where x = a > 0.

m =

(b) Find equations of the tangent lines at the points (1, 7) and (4, 7/2)

y(x)= _________ (at the point (1, 7))

y(x)=_________ (at the point (4, 7/2))



Answer 1

y = 7/x = 7 * x^(-1) = f(x)

y' = -7*x^(-2) = f'(x)

f'(a) = -7 *a^(-2) , a>0

(1,7) ---> m = f'(1) = -7 --> B = y - mx = 7 - (-7)*1 = 14 ---> y = -7x+14

(4, 7/2) = m = -7 * 4 ^(-2) = -7/16 ---> b = y - mx = 7/2 - (-7/16)(4) = 7/2 - (-7/4) = 14/4 + 7/4 = 21/4

y = (-7/16)x + 21/4