Fairly easily. I can surely say we can all agree we don’t want any hard questions. (PS: I have no idea how to use laTeX, so I hope you guys can understand my fail attempt to write a math problem online.)
1) The limit below represents the derivative of f ‘(a). Find the f(x) and the a values.
Lim h->0 of ((3+h)^3) – 27)/h
f(x) = ?
a = ?
2) Find the slope of the secant line through the points of x = 2 and x=4 of the function f(x) = x^2. ( Not sure if I typed this correctly I was half asleep when I woke up: Correct me If I’m wrong)
Slope= ?
1)
![\frac{(3+x)^3-27}{x} \frac{(3+x)^3-27}{x}](https://s0.wp.com/latex.php?latex=%5Cfrac%7B%283%2Bx%29%5E3-27%7D%7Bx%7D&bg=ffffff&fg=000000&s=0)
![\downarrow \downarrow](https://s0.wp.com/latex.php?latex=%5Cdownarrow&bg=ffffff&fg=000000&s=0)
![\frac{(3+x)^3-(3^3)}{x} \frac{(3+x)^3-(3^3)}{x}](https://s0.wp.com/latex.php?latex=%5Cfrac%7B%283%2Bx%29%5E3-%283%5E3%29%7D%7Bx%7D&bg=ffffff&fg=000000&s=0)
![\downarrow \downarrow](https://s0.wp.com/latex.php?latex=%5Cdownarrow&bg=ffffff&fg=000000&s=0)
![f(x)=x^3 f(x)=x^3](https://s0.wp.com/latex.php?latex=f%28x%29%3Dx%5E3&bg=ffffff&fg=000000&s=0)
![f(x)=3x^2 f(x)=3x^2](https://s0.wp.com/latex.php?latex=f%28x%29%3D3x%5E2&bg=ffffff&fg=000000&s=0)
So,
2)
![f(x)=x^2 f(x)=x^2](https://s0.wp.com/latex.php?latex=f%28x%29%3Dx%5E2&bg=ffffff&fg=000000&s=0)
![f(2)=2^2 = 4 f(2)=2^2 = 4](https://s0.wp.com/latex.php?latex=f%282%29%3D2%5E2+%3D+4&bg=ffffff&fg=000000&s=0)
![\downarrow \downarrow](https://s0.wp.com/latex.php?latex=%5Cdownarrow&bg=ffffff&fg=000000&s=0)
![\downarrow \downarrow](https://s0.wp.com/latex.php?latex=%5Cdownarrow&bg=ffffff&fg=000000&s=0)
![m=\frac{detlaY}{deltaX} m=\frac{detlaY}{deltaX}](https://s0.wp.com/latex.php?latex=m%3D%5Cfrac%7BdetlaY%7D%7BdeltaX%7D&bg=ffffff&fg=000000&s=0)
![m=\frac{16-4}{4-2} m=\frac{16-4}{4-2}](https://s0.wp.com/latex.php?latex=m%3D%5Cfrac%7B16-4%7D%7B4-2%7D&bg=ffffff&fg=000000&s=0)
![m=6 m=6](https://s0.wp.com/latex.php?latex=m%3D6&bg=ffffff&fg=000000&s=0)
![\downarrow \downarrow](https://s0.wp.com/latex.php?latex=%5Cdownarrow&bg=ffffff&fg=000000&s=0)
![y-y1 = m(x-x1) y-y1 = m(x-x1)](https://s0.wp.com/latex.php?latex=y-y1+%3D+m%28x-x1%29&bg=ffffff&fg=000000&s=0)
![y-4 = 6(x-2) y-4 = 6(x-2)](https://s0.wp.com/latex.php?latex=y-4+%3D+6%28x-2%29&bg=ffffff&fg=000000&s=0)
![y= 6x-8) y= 6x-8)](https://s0.wp.com/latex.php?latex=y%3D+6x-8%29&bg=ffffff&fg=000000&s=0)
&latex f(4)=4^2 = 16$
so,
(2, 4) , (4, 16)
Sorry, Still trying to learn this latex 🙂