Is anyone good at Basic Rules of Differentiation/Marginal Analysis?

Question

anonymous · Answer

Every single question?

anonymous · Answer

yea, I am totally lost.

amistre64 · Answer

#1, what does each part represent?

amistre64 · Answer

f(x) tells us the amount at any given point

f(x+h)-f(x)
---------  is the average rate of change of an interval
      h

f'(x) is the instantaneous rate of change at any given point

amistre64 · Answer

is that x^x ?

amistre64 · Answer

a convincing arguement might be first principles; but ugh

amistre64 · Answer

g(f(x)) might be more convincing and simpler

anonymous · Answer

i gave up, cus it is too lengthy already to explain haha.

amistre64 · Answer

$$y = x^x$$
$$ln(y)=ln(x^x)$$
$$ln(y)=x ln(x)$$
$$D_x[ln(y)=xln(x)]=\frac{1}{y}y'=x\frac{1}{x}+ln(x)$$
maybe

amistre64 · Answer

so y' = x^x (1+ln(x)) if the wolf will accept it :)

amistre64 · Answer

yay its good lol

amistre64 · Answer

thats all i got

anonymous · Answer

I solved #2 beforet hat for you..

anonymous · Answer

y=f(x)=-15/4x^2+35x+75

anonymous · Answer

# 3)
y=f(x)=-15/4x^2+35x+75

anonymous · Answer

$$f(0)\approx75=c$$
$$f(x)=ax^2+bx+c$$
$$f(6)\approx150$$
$$f(10)\approx50$$
c=75

anonymous · Answer

a=-15/4
b=35
c=75

anonymous · Answer

Thank you!

anonymous · Answer

but func doesnot work well, maybe it is sin func..

anonymous · Answer

or it might be ax^3+bx^2+cx+d