Consider the following fx 4x 1 a 2 a Compute the differen

Consider the following. f(x) = 4/x - 1, a = 2 (a) Compute the difference quotient f(a + h) - f(a)/h at the given value of a. (b) Compute m_tan = lim_h rightarrow 0 f(a + h) - f(a)/h (c) Use the result of part (b) to find an equation of the tangent line at the point of tangency.

Solution

7)

a)f(x)=4/(x-1)

at a =2

f(2)=4/(2-1) =4

f(2+h)=4/(2+h-1)=4/(1+h)

difference coefficient =[f(2+h) -f(2)]_/h

=[(4/(1+h))-4]_/h

=[(4-4-4h)/(1+h)]_/h

=[-4h/(1+h)]_/h

=-4/(1+h)

b)m_tan =lim_h->0[f(2+h) -f(2)]_/h

m_tan =lim_h->0 -4/(1+h)

m_tan =-4/(1+0)

m_tan =-4

c) equation of tangent with slope -4 at point (2,f(2))=(2,4) is

y -4=-4(x-2)

y-4=-4x+8

y =-4x+12

equation of tangent is y =-4x+12