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:
I think x = 44°
Step-by-step explanation:
Finding the exterior angle:
180° - 45° = 135°
We know that x is multiplied by 3 (3x) so we divide 135 by 3.
135° / 3 = 45°
We know that we have to add 3° to the product of 3x, so we know the product of 3x will be less than 135°. The product should be 135° after 3° is added to it.
Trying a few possible answers:
43° × 3 = 129°
129° + 3° = 132°
That one wasn't quite right.
44° × 3 = 132°
132° + 3° = 135°
:D
Rotate the second shape upside down and put the triangle on top