Can anybody help me with this one plz.

Mathematics

1 answer:

Svetradugi [14.3K]2 years ago

7 0

(-1,1)
D0 means starting at the origin of Z in this case, so doing the same thing as always, multiply the scale factor -1/2 to the coordinate of Z giving you (-1,1) and this is the final answer because the origin is (0,0) so doesn’t change anything

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A pet rescue center takes in animals from a local shelter. Half of the animals that they take in are cats.

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3 years ago

Explain why Rolle's Theorem does not apply to the function even though there exist a and b such that f(a)

Anna35 [415]

Rolle's Theorem does not apply to the function because there are points on the interval (a,b) where f is not differentiable.

Given the function is $f(x)=\sqrt{(2-x^{\frac{2}{3}})^{3}}$ and the Rolle's Theorem does not apply to the function.

Rolle's theorem is used to determine if a function is continuous and also differentiable.

The condition for Rolle's theorem to be true as:

f(a)=f(b)
f(x) must be continuous in [a,b].
f(x) must be differentiable in (a,b).

To apply the Rolle’s Theorem we need to have function that is differentiable on the given open interval.

If we look closely at the given function we can see that the first derivative of the given function is:

$\begin{aligned}f(x)&=\sqrt{(2-x^{\frac{2}{3}})^3}\\ f(x)&=(2-x^{\frac{2}{3}})^{\frac{3}{2}}\\ f'(x)&=\frac{3}{2}(2-x^{\frac{2}{3}})^{\frac{1}{2}}\cdot \frac{2}{3}\cdot (-x)^{\frac{1}{3}}\\ f'(x)&=\frac{-\sqrt{2-x^{\frac{2}{3}}}}{\sqrt[3]{x}}\end$