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Tpy6a [65]
3 years ago
12

Let ​ f(x)=x2−3x−4​ . What is the average rate of change from x = 7 to x = 10?

Mathematics
2 answers:
shepuryov [24]3 years ago
8 0

Answer:

The average rate of change from x= 7 to x=10 is 14

Step-by-step explanation:

We can use the slope formula to find the average rate of change

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

Now, we are given f(x) = x^2-3x-4 and x=7 to x=10

Our formula can be rewritten as:

m=\frac{f(10)-f(7)}{10-7}

finding f(10) = (10)^2 -3(10) -4

                   = 100 -30 -4

                   = 66

and f(7) = (7)^2 -3(7) -4

            = 49-21-4

            = 24

Now finding m:

m= 66 - 24 / 10-7

m= 42/3

m= 14

So, the average rate of change from x= 7 to x=10 is 14.

mars1129 [50]3 years ago
4 0

ANSWER

14

EXPLANATION

The given function is

f(x) =  {x}^{2}  - 3x - 4

The average rate of change from x=7 to x=10 is given by;

\frac{f(10) - f(7)}{10 - 7}

f(10) =  {(10)}^{2}  - 3(10) - 4

f(10) =  100  - 30 - 4

f(10) =  66

f(7) =  {7}^{2}  - 3(7) - 4

f(7) = 49 - 21- 4 = 24

The average rate of change now becomes:

\frac{26 - 24}{3}  =  \frac{52}{3} =14

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