g(x)=x^2+3x-1
find (g(x+(delta symbol)x) - g(x)) / ((delta sym)x)

how do I solve this? Please help me!

does the delta symbol mean change in this case? I don't no what to do :(:confused: :mad:

Yes, delta means the 'change in x'. This is the definition of a derivative.

There should be a graph in your calculus book which will help show you what this means.

Except, most times, h is used instead if delta(x). I will use h.

It's based on the slope of a line. The instantaneous rate of change of y with respect to x at

a point x_0 is:

slope=m=\lim_{x_{1}\to\(x_{0})}\frac{f(x_{1})-f(x_{0})}{x_{1}-

x_{0}}

x_{1}-x_{0}=h. Then, x_{1}=x_{0}+h and h approaches 0

as x_{1} approaches x_{0}. Then we can write the slope of

the line as m=\lim_{h\to\0}\frac{f(x_{0}+h)-f(x_{0})}{h}

I will show you how this works and you try another. OK?


\lim_{h\to\0}\frac{f(x+h)-f(x)}{h}

Wherever you have an x, insert x+h. f(x+h)=(x+h)^{2}+3(x+h)-1

You have \lim_{h\to\0}\frac{[(x+h)^{2}+3(x+h)-1]-[x^{2}+3x-1]}{h}

Which simplifies to(you can do the algebra):

\lim_{h\to\0}\frac{2xh+h^{2}+3h}{h}

Now, what do you have as h approaches 0? The derivative of x^{2}+2x-1

g(x)=x^2+3x-1
find (g(x+(delta symbol)x) - g(x)) / ((delta sym)x)

how do i solve this? please help me!

does the delta symbol mean change in this case? i don't no what to do :(:confused: :mad:

Delta is a Greek letter that looks like a triangle on its base. This is one: Δ

Tom