The average rate of change of the function at the interval is -8
<h3>How to determine the average rate of change?</h3>The table that completes the question is added as an attachment
From the table, we have:
f(5) = -26
f(3) = -10
The average rate is then calculated as:
Rate = (f(5) - f(3))/(5 -3)
This gives
Rate = (-26 + 10)/(5 -3)
Evaluate
Rate = -8
Hence, the average rate of change of the function is -8
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Answer:
the one real zero is in the interval (-1, 0)
Step-by-step explanation:
Descartes' rule of signs tells you there are 0 or 2 positive real zeros. Changing the signs of the odd-degree terms and applying that rule again tells you there is one negative real zero. At the same time, those coefficients (-3, -5, -5, +7) have a negative sum, so you know ...
f(-1) = -6
f(0) = +7
so there is a zero in the interval (-1, 0).
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You can try a few values between x=0 and x=10 to see what the function does in that part of the graph. You find ...
f(1) = 10
f(2) = 21
f(3) = 58
So, it is safe to conclude that there are no real zeros for x > 0.
The only real zero of f(x) is in the interval (-1, 0).
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I like to use a graphing calculator for problems like this.
Answer:
Step-by-step explanation:
The given equation is written in the form of y=mx+c (where m is the gradient and c is the y-intercept).
Thus, gradient of given equation= -⅔
The products of the gradient of perpendicular lines is -1.
(Gradient of line)(-⅔)= -1
Gradient of line
Hence, m= .
Subst. m= into the equation:
To find the value of c, substitute a pair of coordinates into the equation:
When x= -4, y= 2,
Thus, the equation of the line is .
