First, write the mixed number as a sum of a whole number and a proper fraction. Then write the two parts with common denominator , and add. Once you're used to this, you can use a shortcut method: 1) Multiply the whole part by the denominator of the fractional part, and add the numerator of the fractional part.
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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2/5
Step-by-step explanation:
4 ÷ 2 = 2
10 ÷ 2 = 5
Answer is 2/5
The new price is 69% i think
Given that Jack biked for
hours with an average speed of
miles per hour.
The distance travelled by Jack is given by
Given that Jim travelled exactly
as far as Jack did, then the distance Jim travelled is given by
Therefore, the length of Jim's journey is 80 miles.
