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Dmitriy789 [7]
4 years ago
9

Determine all critical points for the function. f(x)=(x-10)^5

Mathematics
1 answer:
nikdorinn [45]4 years ago
7 0
A critical point is just where a graph's slope is = to 0, so you can take the derivative of that function and set it equal to 0.

Using the chain rule:
f'(x) = 5(x-10)^4
0 = 5(x-10)^4

divide by 5 on both sides and take the 4th root of both sides.

0 = x - 10

add ten on both sides, and x = 10. Now, plug the x-value back into the original (you want to find the y-value on the original function ,not the derivative).

y = (10-10)^5 = 0

(10,0)
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Starting from the y-intercept of \displaystyle [0, 8],you do \displaystyle \frac{rise}{run}by either moving five blocks <em>north</em> over three blocks <em>west</em> or five blocks <em>south</em> over three blocks <em>east</em> [<em>west</em> and <em>south</em> are negatives].

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