Mathematics, 17.05.2021 14:00 cameronbeaugh

A function is given by f(x) =
Evaluate f'(16).

$\sqrt[4]{x}$

Answers: 2

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Answers

Answer from: perezkeirax33K

$\displaystyle f'(16) = \frac{1}{32}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Algebra I

Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$ Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

$\displaystyle f(x) = \sqrt[4]{x}$

f'(16) is x = 16 for the derivative f'(x)

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle f(x) = x^{\frac{1}{4}}$ Basic Power Rule: $\displaystyle f'(x) = \frac{1}{4}x^{\frac{1}{4} - 1}$ Simplify: $\displaystyle f'(x) = \frac{1}{4}x^{\frac{-3}{4}}$ Rewrite [Exponential Rule - Rewrite]: $\displaystyle f'(x) = \frac{1}{4x^{\frac{3}{4}}}$

Step 3: Solve

Substitute in x [Derivative]: $\displaystyle f'(16) = \frac{1}{4(16)^{\frac{3}{4}}}$ Evaluate exponents: $\displaystyle f'(16) = \frac{1}{4(8)}$ Multiply: $\displaystyle f'(16) = \frac{1}{32}$

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e

Answer from: Quest

A) 144.44 sq inches i believe
20 points angela decides to recycle a large oatmeal container by using it to hold a friends birthd

Answer from: Quest

$\frac{1}{12}$

step-by-step explanation:

a cube has 6 sides

the probability of getting 5 on the first cube is 1/6 since only one side of the cube has 5 on it.

there are 3 sides of the cube with even number on it [2,4,6]

therefore the probability of getting even number is 3/6

for both events to happen together, the probability would be

1/6 x 3/6 = 12/36

which simplifies to 1/12

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A function is given by f(x) =

Evaluate f'(16)....

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