Mathematics, 28.10.2020 15:00 baby0905rodriguez

MULTIPLE CHOICE CALCULUS 1) An object moves along a line so that its position at time t is s(t) = t^4 - 6t^3 - 2t - 1.

At what time t is the acceleration of the object zero?

A. at 3 only

B. at 0 and 3 only

C. at 0 only

D. at 1 only

2) If f(x) = e^x (sin x + cos x), then f'(x) =

A. 2e^x (cos x + sin x)

B. e^x cos x

C. e^x (cos^2x - sin^2x)

D. 2e^x cos x

Answers: 1

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Answers

Answer from: arubright177

1) B. at 0 and 3 only

2) D. 2eˣcosx

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Terms/CoefficientsFactoringQuadratics

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Trig Derivative: $\displaystyle \frac{d}{dx}[sinu] = u'cosu$

Trig Derivative: $\displaystyle \frac{d}{dx}[cosu] = -u'sinu$

eˣ Derivative: $\displaystyle \frac{d}{dx} [e^u]=e^u \cdot u'$

Step-by-step explanation:

*Note:

Velocity is the derivative of position.

Acceleration is the derivative of velocity.

Question 1

Step 1: Define

s(t) = t⁴ - 6t³ - 2t - 1

Step 2: Differentiate

[Velocity] Basic Power Rule: s'(t) = 4 · t⁴⁻¹ - 3 · 6t³⁻¹ - 1 · 2t¹⁻¹[Velocity] Simplify: v(t) = 4t³ - 18t² - 2[Acceleration] Basic Power Rule: v'(t) = 3 · 4t³⁻¹ - 2 · 18t²⁻¹[Acceleration] Simplify: a(t) = 12t² - 36t

Step 3: Solve

[Acceleration] Set up: 12t² - 36t = 0[Time] Factor: 12t(t - 3) = 0[Time] Identify: t = 0, 3

Question 2

Step 1: Define

f(x) = eˣ(sinx + cosx)

Step 2: Differentiate

[Derivative] Product Rule: $\displaystyle f'(x) = \frac{d}{dx}[e^x](sinx + cosx) + e^x\frac{d}{dx}[sinx + cosx]$ [Derivative] Rewrite [Derivative Property - Addition]: $\displaystyle f'(x) = \frac{d}{dx}[e^x](sinx + cosx) + e^x(\frac{d}{dx}[sinx] + \frac{d}{dx}[cosx])$ [Derivative] eˣ Derivative: $\displaystyle f'(x) = e^x(sinx + cosx) + e^x(\frac{d}{dx}[sinx] + \frac{d}{dx}[cosx])$ [Derivative] Trig Derivatives: $\displaystyle f'(x) = e^x(sinx + cosx) + e^x(cosx - sinx)$ [Derivative] Factor: $\displaystyle f'(x) = e^x[(sinx + cosx) + (cosx - sinx)]$ [Derivative] Combine like terms: $\displaystyle f'(x) = e^x[2cosx]$ [Derivative] Multiply: $\displaystyle f'(x) = 2e^xcosx$

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

Unit: Derivatives

Book: College Calculus 10e

Answer from: Quest

109 is the nearest whole number/final answer! : )

Answer from: Quest

31/6= 19/6 19/6 *1/7=19/42

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MULTIPLE CHOICE CALCULUS 1) An object moves along a line so that its position at time t is s(t) = t...

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