Homework Statement
find the inflection points of x^2-4√x
Homework EquationsThe Attempt at a Solution
Okay, I started with finding the derivatives;
f'(x)=2x-2/√x
f''(x)=2+1/√x^3
and made the second derivative =0
(2+1/√x^3=0)(√x^3)
2√x^3+1=0
(√x^3=-1/2)^2
x^3=1/4
x=cube root(1/4)
x=0.63
But when...
Homework Statement
if f(x)=sin(x), evaluate lim h→0 (f(2+h)-f(2))/h) to two decimal places
Homework Equations
(f(x+h)-f(x))/h
The Attempt at a Solution
On the assumption that this is the same as lim x→2 sin(x)
sin(2)=0.91
okay, is there an easier way of combining the exponential binomials or do i have to expand all of them out completely and try to find a way to factor them back down?
Homework Statement
6(2x+5)^2(6x-1)^5+(2x+5)^3(30)(6x-1)^4
this is what i got from deriving (2x+5)^3(6x-1)^5 and now i have to express my answer in factored form, does this classify as factored from even though it has a '+' in it?
Homework EquationsThe Attempt at a Solution
i suppose what I am asking would be; what does dy/dt mean? I can't wrap my head around the explanation in my textbook and I am looking for a dumbed down version
i understand differentiation in that you could find the derivative by going (2*1)t^(1-1) =2 I'm not clear on how it relates to dy/dt and combining it with dx/dt
Homework Statement
if y=2t+3 and x=t^2, find dy/dx
Homework Equations
dy=dy/dt*dt/dx
The Attempt at a Solution
dy/dt=2
dx/dt=2t
therefore dy/dx=1/t
what I don't understand is how the dy/dt etc. is found when attempting this problem[/B]
I believe it because the limits approaching 1 from the left and right side is -2, what i don't understand is if and where the 'f(x)=3 when x=1' comes into play