Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

For the following equation, what is the instantaneous rate of change at x=-2? f(x)=-x^(3)-2x Answer:

For the following equation, what is the instantaneous rate of change at x=−2? x=-2 ? \newlinef(x)=−x3−2x f(x)=-x^{3}-2 x \newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Calculusright chevron icon
Find derivatives using logarithmic differentiationright chevron icon

Full solution

Q. For the following equation, what is the instantaneous rate of change at x=−2? x=-2 ? \newlinef(x)=−x3−2x f(x)=-x^{3}-2 x \newlineAnswer:
  1. Calculate Derivative: To find the instantaneous rate of change of the function at a specific point, we need to calculate the derivative of the function. The derivative of a function at a point gives us the slope of the tangent line at that point, which is the instantaneous rate of change.
  2. Apply Power Rule: The function given is f(x)=−x3−2xf(x) = -x^3 - 2x. We will find the derivative f′(x)f'(x) using the power rule. The power rule states that the derivative of xnx^n is n⋅x(n−1)n\cdot x^{(n-1)}.
  3. Evaluate at x=−2x = -2: Applying the power rule to each term in the function:\newlineThe derivative of −x3-x^3 is −3x2-3x^2 (using the power rule).\newlineThe derivative of −2x-2x is −2-2 (since the derivative of xx is 11 and the constant multiple rule applies).\newlineSo, f′(x)=−3x2−2f'(x) = -3x^2 - 2.
  4. Substitute and Calculate: Now we need to evaluate the derivative at x=−2x = -2 to find the instantaneous rate of change at that point.\newlineSubstitute x=−2x = -2 into f′(x)f'(x):\newlinef′(−2)=−3(−2)2−2f'(-2) = -3(-2)^2 - 2.
  5. Substitute and Calculate: Now we need to evaluate the derivative at x=−2x = -2 to find the instantaneous rate of change at that point.\newlineSubstitute x=−2x = -2 into f′(x)f'(x):\newlinef′(−2)=−3(−2)2−2f'(-2) = -3(-2)^2 - 2.Calculate the value:\newlinef′(−2)=−3(4)−2=−12−2=−14f'(-2) = -3(4) - 2 = -12 - 2 = -14.

More problems from Find derivatives using logarithmic differentiation

Question
Convert. \newline 500500 milligrams == _____ grams
Get tutor helpright-arrow

Posted 9 months ago

Question
Convert. \newline 2,0002,000 milligrams == _____ grams
Get tutor helpright-arrow

Posted 9 months ago

Question
Convert. \newline 750750 milligrams == _____ grams
Get tutor helpright-arrow

Posted 9 months ago

Question
Convert. \newline1,5001,500 milligrams == _____ grams
Get tutor helpright-arrow

Posted 9 months ago

Question
Convert. \newline1,5001,500 milligrams == _____ grams
Get tutor helpright-arrow

Posted 9 months ago

Question
According to Newton's Second Law of Motion, the sum of the forces that act on an object with a mass mm that moves with an acceleration aa is equal to m⋅am \cdot a. An object whose mass is 8080 grams has an acceleration of 2020 meters per seconds squared. What calculation will give us the sum of the forces that act on the object, in Newtons (which are kg⋅ms2\frac{\text{kg} \cdot \text{m}}{\text{s}^2})?\newlineChoose 11 answer:\newline(A) 80⋅2080 \cdot 20\newline(B) 80⋅1000⋅2080 \cdot 1000 \cdot 20\newline(C) 801000⋅20\frac{80}{1000} \cdot 20\newline(D) 80602⋅20\frac{80}{60^2} \cdot 20
Get tutor helpright-arrow

Posted 8 months ago

Question
Simplify.\newlineMultiply and remove all perfect squares from inside the square roots. Assume \newlineb b is positive.\newline28b3⋅918b= 2\sqrt{8b^{3}} \cdot 9\sqrt{18b} =
Get tutor helpright-arrow

Posted 10 months ago

Question
Roselyn is driving to visit her family, who live 150150 kilometers away. Her average speed is 6060 kilometers per hour. The car's tank has 2020 liters of fuel at the beginning of the drive, and its fuel efficiency is 66 kilometers per liter. Fuel costs 0.600.60 dollars per liter.\newlineHow long can Roselyn drive before she runs out of fuel?\newlinehours
Get tutor helpright-arrow

Posted 10 months ago

Question
Astrid is in charge of building a new fleet of ships. Each ship requires 4040 tons of wood, and accommodates 300300 sailors. She receives a delivery of 44 tons of wood each day. The deliveries can continue for 100100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 21002100 sailors.\newlineHow much wood does Astrid need to accommodate 21002100 sailors?\newlinetons
Get tutor helpright-arrow

Posted 10 months ago

Question
Lily's car has a fuel efficiency of 8 liters8 \text{ liters} per 100 kilometers100 \text{ kilometers}.\newlineWhat is the fuel efficiency of Lily's car in kilometers\text{kilometers} per liter\text{liter}?\newlinekmL\frac{\text{km}}{\text{L}}
Get tutor helpright-arrow

Posted 10 months ago

View all (38)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant