The instantaneous rate of change of the function f(x) = −4x² − 3x + 1 at the point x = -3 is 21.
<h3>What is the instantaneous rate of change of the function at the given point?</h3>
The instantaneous rate of change is simply the change in the derivative value at a specific point.
Given the data in the question;
- f(x) = −4x² − 3x + 1
- Point x = -3
To determine the instantaneous rate of change of the function, first find the derivative of the function.
f(x) = −4x² − 3x + 1
Applying sum rule, with respect to x
d/dx[ -4x² ] + d/dx[ -3x ] + d/dx[ 1 ]
[ 2 × -4x¹ ] + [ 1 × -3x⁰ ] + d/dx[ 1 ]
[ -8x ] + [ -3 ] + d/dx[ 1 ]
-8x - 3 + d/dx[ 1 ]
Differentiate using constant rule
-8x - 3 + [ 0 ]
-8x - 3
f'(x) = -8x - 3
Next, plug x = -3 into the derivative and simplify.
f'(x) = -8x - 3
f'(-3) = -8(-3) - 3
f'(-3) = 24 - 3
f'(-3) = 21
Therefore, the instantaneous rate of change of the function f(x) = −4x² − 3x + 1 at the point x = -3 is 21.
Learn more about instantaneous rate of change here: brainly.com/question/28122560
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Answer:
A coefficient number is a number multiplied by a variable.
Step-by-step explanation:
Answer:
1 3/5
Step-by-step explanation:
Anything larger than 1 multiplied by 3 1/4 would result in a number more than 3 1/4.
Answer: -12
Step-by-step explanation: To solve this problem, we can first start by rewriting the problem. When we add a negative, that's exactly the same thing as subtracting so we can make the problem easier to understand.
18 + (-30) → 18 - 30
To find the answer to this problem, let's first find out how many jumps it get's to 0 from 18. It would take 18 jumps and there is 12 jumps left over. Then, we would subtract 12 from 0 and we would get -12 as our answer. Therefore, 18 + (-30) = -12.
