The function f(x) = 2x³ − 42x² + 270x - 7 has two critical numbers. Use the derivative to algebraically find the critical numbers. The smaller one equals and The larger one equals Hint: Factor carefully.

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A: Given function have to find the directional derivative in the direction of vector .As we know -

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Q: Solve the equation and check your solution. 5x − 14 3 X = 15+X -2 +4

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Q: 8. Find the derivative of each. N (a) y = sin-¹(x³)

A: Since you have asked multiple questions in a single request so we will be answering only first…

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Q: For the functions f(x) NOTE: Enter the exact answers (a) f(g(1)) = (b) g(f(1)) = (c) f(g(x)) = (d)…

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A: Elasticity,E(p) = Where D(p) is the demand function.

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A: we need to find out the double derivative of the given expression.

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A: The curve of the function f(x) is shown as,

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A: Given,

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A: To solve part d and part e, answer of part c is required.

Q: 2. Determine d (sin-¹(x²-1)). dx Simplify your answer as much as possible.

A: Consider the function

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A: The function is  Here we have to find the derivative of the function

Q: Find the derivative for each of the following inverse trig. functions. (a) dª arctan(7x) = dr (b)…

A: We know,

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Q: For the demand function q = D(p) = 344 - p, find the following. a) The elasticity b) The elasticity…

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Q: Find the GCF of the expressions. 12x¹4yz6, 24x6z8, and 4xyz7

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Q: 5x+500 A garden shop determines the demand function q = D(x) = 20x +9 the number of plants sold per…

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A: Given, .Given,  f(0)=2, f'(0)=18.We know,

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Q: ex - 32 √x +x 22

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A: The region enclosed by planes

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A: This is a special type of differential equation which is called the Cauchy-Euler differential…

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A: Given, .

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A: Using determinant, we can find the area.

Q: In 2005, a school population was 1708. By 2006 the population had grown to 1776. 1) How much did the…

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