Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

For the following equation, what is the instantaneous rate of change at
x=-1?

f(x)=-3x^(2)+2
Answer:

For the following equation, what is the instantaneous rate of change at $x=-1 ?$ $\newline$ $f(x)=-3 x^{2}+2$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Find derivatives using logarithmic differentiation

Full solution

Q. For the following equation, what is the instantaneous rate of change at

x=-1 ?

\newline

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

\newline

Answer:

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 gives us the slope of the tangent line at any point, which is the instantaneous rate of change.
Apply Power Rule: The function given is $f(x) = -3x^2 + 2$ . To find its derivative, we use the power rule, which states that the derivative of $x^n$ is $n\cdot x^{(n-1)}$ . Applying this rule to each term in the function, we get: $\newline$ $f'(x) = \frac{d}{dx}(-3x^2) + \frac{d}{dx}(2)$ $\newline$ $f'(x) = -3 \cdot 2x^{(2-1)} + 0$ $\newline$ $f'(x) = -6x$
Find Instantaneous Rate: Now that we have the derivative, we can find the instantaneous rate of change at $x = -1$ by plugging $-1$ into the derivative function. $\newline$ $f'(-1) = -6*(-1)$ $\newline$ $f'(-1) = 6$

More problems from Find derivatives using logarithmic differentiation

Question

\newline

\sqrt{\frac{9}{25}}

\newline

Posted 3 months ago

Question

\newline

1,000

\text{ milligrams}

\_\_\_\_

\text{ grams}

Posted 3 months ago

Question

3

-gallon bottle of bleach costs

\$11.52

. What is the price per quart?

\newline

Posted 3 months ago

Question

Maureen can't wait to make chocolate chip zucchini bread with zucchini from her garden. Her recipe calls for

8

ounces of chocolate chips per loaf. If she has enough zucchini to make

4

loaves of zucchini bread, how many pounds of chocolate chips does she need?

\newline

Hint: There are

16

1

\newline

Write your answer as a whole number, decimal, or simplified fraction. Do not round.

\newline

Posted 3 months ago

Question

A whale is swimming due north at a speed of

30

miles per hour. Just

5

miles away, a whale-watching tour boat is traveling south, directly toward the whale, at a speed of

46

miles per hour. How long will it be before they meet? If necessary, round your answer to the nearest minute.

\_\_\_\_

\_\_\_\_

Posted 3 months ago

Question

\newline

500

=

Posted 4 months ago

Question

\newline

2,000

=

Posted 4 months ago

Question

\newline

750

=

Posted 4 months ago

Question

\newline

1,500

=

Posted 4 months ago

Question

\newline

1,500

=

Posted 4 months ago