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:

Find the average rate of change of k(x)=xk(x) = x between x=4x = 4 and x=4+hx = 4 + h, where h≠0h \neq 0.\newlineSimplify your answer. Your answer may be a number or an expression in terms of hh.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Average rate of change IIright chevron icon

Full solution

Q. Find the average rate of change of k(x)=xk(x) = x between x=4x = 4 and x=4+hx = 4 + h, where h≠0h \neq 0.\newlineSimplify your answer. Your answer may be a number or an expression in terms of hh.
  1. Understand formula: First, we need to understand the formula for the average rate of change, which is (k(x2)−k(x1))/(x2−x1)(k(x_2) - k(x_1)) / (x_2 - x_1). Here, x1=4x_1 = 4 and x2=4+hx_2 = 4 + h.
  2. Substitute values: Substitute the values into the function k(x)=xk(x) = x. So, k(4)=4k(4) = 4 and k(4+h)=4+hk(4 + h) = 4 + h.
  3. Plug into formula: Plug these values into the average rate of change formula: (4+h)−4(4+h)−4\frac{(4 + h) - 4}{(4 + h) - 4}.
  4. Simplify numerator and denominator: Simplify the numerator and the denominator: h/hh / h.
  5. Cancel out hh: Since h≠0h \neq 0, we can simplify further by canceling out hh in the numerator and denominator, which gives us 11.

More problems from Average rate of change II

Question
Consider the curve given by the equation xy2+5xy=50 x y^{2}+5 x y=50 . It can be shown that dydx=−y(y+5)x(2y+5).  \frac{d y}{d x}=\frac{-y(y+5)}{x(2 y+5)} \text {. } \newlineWrite the equation of the vertical line that is tangent to the curve.
Get tutor helpright-arrow

Posted 5 months ago

Question
What is the value of ddx(x−3) \frac{d}{d x}\left(x^{-3}\right) at x=3 x=3 ?
Get tutor helpright-arrow

Posted 7 days ago

Question
The rate of change dPdt \frac{d P}{d t} of the number of algae in a tank is modeled by the following differential equation:\newlinedPdt=231710614P(1−P662) \frac{d P}{d t}=\frac{2317}{10614} P\left(1-\frac{P}{662}\right) \newlineAt t=0 t=0 , the number of algae in the tank is 174174 and is increasing at a rate of 2828 algae per minute. At what value of P P is P(t) P(t) growing the fastest?\newlineAnswer:
Get tutor helpright-arrow

Posted 6 months ago

Question
The rate of change dPdt \frac{d P}{d t} of the number of bacteria in a tank is modeled by the following differential equation:\newlinedPdt=29849P(598−P) \frac{d P}{d t}=\frac{2}{9849} P(598-P) \newlineAt t=0 t=0 , the number of bacteria in the tank is 196196 and is increasing at a rate of 1616 bacteria per minute. At what value of P P does the graph of P(t) P(t) have an inflection point?\newlineAnswer:
Get tutor helpright-arrow

Posted 6 months ago

Question
The rate of change dPdt \frac{d P}{d t} of the number of people infected by a disease is modeled by the following differential equation:\newlinedPdt=45125404P(800−P) \frac{d P}{d t}=\frac{45}{125404} P(800-P) \newlineAt t=0 t=0 , the number of people infected by the disease is 214214 and is increasing at a rate of 4545 people per hour. What is the limiting value for the total number of people infected by the disease as time increases?\newlineAnswer:
Get tutor helpright-arrow

Posted 6 months ago

Question
The exponential function f f is graphed in the xy x y -plane. As x x increases by 1,y 1, y increases by a factor of 33 . Which of the following could be f f ?\newlineChoose 11 answer:\newline(A) f(x)=(13)x f(x)=\left(\frac{1}{3}\right)^{x} \newline(B) f(x)=(13)x+3 f(x)=\left(\frac{1}{3}\right)^{x}+3 \newline(C) f(x)=3x+2 f(x)=3^{x}+2 \newline(D) f(x)=2(3)x f(x)=2(3)^{x}
Get tutor helpright-arrow

Posted 3 days ago

Question
Which of the following is a correct interpretation of the expression \newline−4+13-4+13?\newlineChoose 11 answer:\newline(A) The number that is 44 to the left of −13-13 on the number line\newline(B) The number that is 44 to the right of −13-13 on the number line\newline(C) The number that is 1313 to the left of −4-4 on the number line\newline(D) The number that is 1313 to the right of −4-4 on the number line
Get tutor helpright-arrow

Posted 6 months ago

Question
The function f f is defined by f(x)=x3+2sin⁡(3x−3) f(x)=x^{3}+2 \sin (3 x-3) . Use a calculator to write the equation of the line tangent to the graph of f f when x=0.5 x=0.5 . You should round all decimals to 33 places.\newlineAnswer:
Get tutor helpright-arrow

Posted 6 months ago

Question
The function f f is defined by f(x)=x2−2x+3cos⁡(x2−x) f(x)=x^{2}-2 x+3 \cos \left(x^{2}-x\right) . Use a calculator to write the equation of the line tangent to the graph of f f when x=−2.5 x=-2.5 . You should round all decimals to 33 places.\newlineAnswer:
Get tutor helpright-arrow

Posted 6 months ago

Question
The function f f is defined by f(x)=x2+x−2sin⁡(2x) f(x)=x^{2}+x-2 \sin (2 x) . Use a calculator to write the equation of the line tangent to the graph of f f when x=3 x=3 . You should round all decimals to 33 places.\newlineAnswer:
Get tutor helpright-arrow

Posted 6 months ago

View all (8)

Related topics

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