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rjkz [21]
2 years ago
13

Consider the function f ( x ) = 1 − 4 x 2 on the interval [ − 1 , 3 ] . Find the average or mean slope of the function on this i

nterval, i.e. f ( 3 ) − f ( − 1 ) 3 − ( − 1 ) =
Mathematics
1 answer:
Blababa [14]2 years ago
4 0

Answer:

The average slope is 8.

Step-by-step explanation:

Let <em>f</em> be defined on the closed interval [a, b]. The average slope of <em>f </em>between a and b is the quotient

                                       average slope = \frac{f(b)-f(a)}{b-a}

To find the average slope of the function f(x)=1-4x^2 on the interval [-1, 3] you have to evaluate your function in the interval and then divide by the interval.

So,

f(-1)=1-4(-1)^2=-3\\\\f(3)=1-4(3)^2=-35

The average slope is  \frac{f(3)-f(-1)}{3+1}= \frac{-3+35}{3+1}=\frac{32}{4}=8

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