i need help with all parts of question 3 and 4. here is a pic of the problems

http://imgur.com/F44GY9Z

please include all work in the answers. thanks in advance

f(x)=100,000+2000t^{2}

f’(x)= 4000t

f’(10) = 4000*10 =40000= 40,000

x

h

f(x)

Diff quot

10

0.1

304020

300000

40200

0.5

320500

41000

0.05

302005

40100

0.01

300400.2

40020

0.001

300040

40002

0.0001

300004

40000.2

We can see the diff quotient approaches 40000

g(x) =1/x

Tangent x= 1 and x= -2

Slope of tangent at x=1 is g’(x) at x=1

g’(x) = -1/x^{2} ; g’(1) = -1

g’(-2) = -1/(-2)^{2 } =-1/4

Equation of the tangent at x=1 and y =1/x =1is

(y-1)= -1(x-1)

y-1+x-1=0

y+x =2

or y =-x+2

Equation of the tangent at x= -2 and y =-1/2 is

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

y+1/2 = -1/4 *x+1/2

y = -x/4

[ f(1+h)-f(1)]/h = [1/(1+h) -1] /h

=(1-(h+1))/[h(h+1)]= -h/[h(h+1)] =-1/(h+1) -> -1 as h->0

[ f(-2+h)-f(-2)]/h = [1/(-2+h) -1/(-2)] /h

= [1/(-2+h) +1/2] /h

=(2+1(-2+h))/[2(-2+h]= h/[h[2(-2+h)] =

-1/[2(-2+h)] -> -1/4 as h->0

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