Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the average rate of change of $f(x) = -10x^2$ between $x = 0$ and $x = h$ , where $h \neq 0$ . $\newline$ Simplify your answer. Your answer may be a number or an expression in terms of $h$ .

View step-by-step help

View step-by-step help

Average rate of change II

Full solution

Q. Find the average rate of change of

f(x) = -10x^2

between

x = 0

and

x = h

, where

h \neq 0

.

\newline

Simplify your answer. Your answer may be a number or an expression in terms of

h

.

Identify Function and Points: Identify the function and points for calculating the average rate of change. $\newline$ Function: $f(x) = -10x^2$ $\newline$ Points: $x = 0$ and $x = h$
Calculate $f(0)$ and $f(h)$ : Calculate $f(0)$ and $f(h)$ .
$f(0) = -10(0)^2 = 0$
$f(h) = -10(h)^2 = -10h^2$
Use Average Rate of Change Formula: Use the formula for average rate of change: $(f(b) - f(a)) / (b - a)$ . Substitute $a = 0$ , $b = h$ , $f(0) = 0$ , and $f(h) = -10h^2$ . Average rate of change = $(f(h) - f(0)) / (h - 0) = (-10h^2 - 0) / h$
Simplify the Expression: Simplify the expression. $\newline$ Average rate of change = $\frac{-10h^2}{h} = -10h$

More problems from Average rate of change II

Question

Consider the curve given by the equation

x y^{2}+5 x y=50

. It can be shown that

\frac{d y}{d x}=\frac{-y(y+5)}{x(2 y+5)} \text {. }

\newline

Write the equation of the vertical line that is tangent to the curve.

Posted 5 months ago

Question

What is the value of

\frac{d}{d x}\left(x^{-3}\right)

x=3

Posted 7 days ago

Question

The rate of change

\frac{d P}{d t}

of the number of algae in a tank is modeled by the following differential equation:

\newline

\frac{d P}{d t}=\frac{2317}{10614} P\left(1-\frac{P}{662}\right)

\newline

t=0

, the number of algae in the tank is

174

and is increasing at a rate of

28

algae per minute. At what value of

P

P(t)

growing the fastest?

\newline

Posted 6 months ago

Question

The rate of change

\frac{d P}{d t}

of the number of bacteria in a tank is modeled by the following differential equation:

\newline

\frac{d P}{d t}=\frac{2}{9849} P(598-P)

\newline

t=0

, the number of bacteria in the tank is

196

and is increasing at a rate of

16

bacteria per minute. At what value of

P

does the graph of

P(t)

have an inflection point?

\newline

Posted 6 months ago

Question

The rate of change

\frac{d P}{d t}

of the number of people infected by a disease is modeled by the following differential equation:

\newline

\frac{d P}{d t}=\frac{45}{125404} P(800-P)

\newline

t=0

, the number of people infected by the disease is

214

and is increasing at a rate of

45

people per hour. What is the limiting value for the total number of people infected by the disease as time increases?

\newline

Posted 6 months ago

Question

The exponential function

f

is graphed in the

x y

x

1, y

increases by a factor of

3

. Which of the following could be

f

\newline

1

\newline

f(x)=\left(\frac{1}{3}\right)^{x}

\newline

f(x)=\left(\frac{1}{3}\right)^{x}+3

\newline

f(x)=3^{x}+2

\newline

f(x)=2(3)^{x}

Posted 3 days ago

Question

Which of the following is a correct interpretation of the expression

\newline

-4+13

\newline

1

\newline

(A) The number that is

4

-13

on the number line

\newline

(B) The number that is

4

to the right of

-13

on the number line

\newline

(C) The number that is

13

-4

on the number line

\newline

(D) The number that is

13

to the right of

-4

on the number line

Posted 6 months ago

Question

f

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

x=0.5

. You should round all decimals to

3

\newline

Posted 6 months ago

Question

f

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

x=-2.5

. You should round all decimals to

3

\newline

Posted 6 months ago

Question

f

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

x=3

. You should round all decimals to

3

\newline

Posted 6 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant