Answer:
The slope of the line is
.
Step-by-step explanation:
We use the formula change in y over change in x to find the slope:
![\frac{5-4}{2-6}](https://tex.z-dn.net/?f=%5Cfrac%7B5-4%7D%7B2-6%7D)
Then we simplify:
![\frac{1}{-4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B-4%7D)
The slope of the line is
.
Answer:a
Step-by-step explanation:
it became wider by decreasing two on the graph.
Answer:
6 5/6
Step-by-step explanation:
diameter is radius multiplied by 2
* means multiplied by
3 5/12 = 41/12
41/12 * 2 = 82/12 = 6 5/6
If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate
.
We have
![\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%20x%5E4%20%3D%20%5Cdisplaystyle%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B%28x%2Bh%29%5E4%20-%20x%5E4%7Dh)
Expand the numerator using the binomial theorem, then simplify and compute the limit.
![\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%20x%5E4%20%3D%20%5Cdisplaystyle%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B%28x%5E4%2B4hx%5E3%20%2B%206h%5E2x%5E2%20%2B%204h%5E3x%20%2B%20h%5E4%29%20-%20x%5E4%7Dh%20%5C%5C%5C%5C%20~~~~~~~~%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B4hx%5E3%20%2B%206h%5E2x%5E2%20%2B%204h%5E3x%20%2B%20h%5E4%7Dh%20%5C%5C%5C%5C%20~~~~~~~~%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%284x%5E3%20%2B%206hx%5E2%20%2B%204h%5E2x%20%2B%20h%5E3%29%20%3D%20%5Cboxed%7B4x%5E3%7D)
In general, the derivative of a power function
is
. (This is the aptly-named "power rule" for differentiation.)
Answer:
if you go on https://www.geogebra.org/ it will graph it for you
Step-by-step explanation: