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2 years ago

The function y=f(x) is graphed below. What is the average rate of change of the function f(x) on the interval -3 ≤ x ≤ 6

Mathematics

1 answer:

victus00 [196]2 years ago

4 0

Answer:

Average ROC = 0

Step-by-step explanation:

Average ROC : (f(b) - f(a)) / (b - a) ... slope = (y'-y) / (x'-x)

a = -3 f(a) = 10 ... x=-3, y=10

b = 6 f(b) = 10 ... x'=6, y'=10

Average ROC = (10 - 10) / (6 - -3) = 0 / 9 = 0

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2 years ago

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lora16 [44]

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$1 \le r \le \sqrt2$ means our region is between two cylinders with radius 1 and $\sqrt2$ . In spherical coordinates, the inner cylinder has equation

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This cylinder meets the sphere when

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which occurs at

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Putting everything together, we have

$\displaystyle \int_0^{2\pi} \int_1^{\sqrt2} \int_{-\sqrt{2-r^2}}^{\sqrt{2-r^2}} r \, dz \, dr \, d\theta = \boxed{\int_0^{2\pi} \int_{\pi/4}^{3\pi/4} \int_{\csc(\phi)}^{\sqrt2} \rho^2 \sin(\phi) \, d\rho \, d\phi \, d\theta} = \frac{4\pi}3$

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2 years ago

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