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.
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Answer:
4 minutes 5 seconds
Step-by-step explanation:
Without additional information, we have to assume that one sequence can begin immediately after another, and that each takes the same amount of time. The total time for 7 sequences is 7 times the time for one sequence.
7 × 35 seconds = 245 seconds = 4 minutes 5 seconds
__
There are 60 seconds in a minute.
Answer: There are 2 batteries which he can buy with his earnings .
Step-by-step explanation:
Since we have given that
Selling price of cans at the recycling center = $0.40 per pound
Number of pounds of cans he sold on Monday = 16.2
Number of pounds of cans he sold on Tuesday = 11.8
Total earning of Samuel is given by
Now, cost of battery =$5.60
So, number of batteries he can buy is given by
So, there are 2 batteries which he can buy with his earnings .
Answer:
You forgot to post your mistake.
Step-by-step explanation:
Sample Equation: 3x - 3 = 27
Multiple step:
3x - 3 = 27
<u> + 3 +3</u> Step1. Remove the -3 by adding 3 to both sides
3x = 30
<u>÷3 ÷ 3</u> Step2. Remove the multiplicand 3 by dividing both sides by 3
x = 10
To check: substitute x by its value
3x - 3 = 27
3(10) - 3 = 27
30 - 3 = 27
27 = 27
