Question
Asked Oct 10, 2019
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Find all relative extrema of the function. (If an answer does not exist, enter DNE.)

f(x) = −4x2 + 5x + 8
relative maximum     (x, y)  = 
 
 
 
 
 
 
 
relative minimum     (x, y)  =   
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Expert Answer

Step 1

Finding f’(x)

 

To find the relative extremum points of the function, we must use first derivative of the function,

 

f'(x)=-8x+5
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f'(x)=-8x+5

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Step 2

Finding all the critical points and all points where f is undefined.

 

The critical points of a function f are x-values within the domain of f for which f’(x) = 0 or

 

Where the function is defined and its derivative is zero and undefined.

 

So, critical points are:

f'(x) 0
-8x5 0
5
x =
8
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f'(x) 0 -8x5 0 5 x = 8

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Step 3

Analysing intervals of increase or decrease:

 

T...

interval
f(x)
Test x-value
Conclusion
5
-ox<=
8
f(-1)13>0increasing
x =-1
5
8
8
5
x< 8
f (1)-3<0 decreasing
nco
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interval f(x) Test x-value Conclusion 5 -ox<= 8 f(-1)13>0increasing x =-1 5 8 8 5 x< 8 f (1)-3<0 decreasing nco

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Tagged in

Math

Calculus