HELP: Find the equation of the linear function represented by the table below in slope-intercept form. (image included)
1 answer:
Given:
The table of value of a linear function.
To find:
The linear function in slope intercept form.
Solution:
Slope intercept form:
Where, m is slope and b is y-intercept.
Consider any two points from the given table.
It is clear that the linear function passes through the points (1,0) and (2,5). So, the equation of the linear function is
Using distributive property, we get
Therefore, the slope intercept form of the given linear function is .
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Answer:
(A)The absolute maximum of f(x) is at x=5
Step-by-step explanation:
F(x)=−2x³+21x²−60x on [1,6]
Find the first derivative.
f'(x)=-6x²+42x-60
Set the first derivative equal to zero.
-6x²+42x-60=0
Solve to find the critical points.
x=2,5
Next, we use the endpoints and all critical points on the interval to test for any absolute extrema over the given interval.
x=1,2,5,6
This is done by evaluating the function at x=1,2,5,6.
F(1)=−2(1)³+21(1)²−60(1)=-41
F(2)=−2(2)³+21(2)²−60(2)=-52
F(5)=−2(5)³+21(5)²−60(5)=-25
F(6)=−2(6)³+21(6)²−60(6)=-36
The maximum will occur at the highest f(x) value and the minimum will occur at the lowest f(x) value.
Absolute Maximum: (5,-25)
Absolute Minimum: (2,-52)
The graph is attached.
The absolute minimum and maximum of f(x) are (2,-52) and (5,-25) respectively.
