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ok so I have three questions I am struggling with.

 

1.) The table of values represents a polynomial function f (x). 

How much greater is the average rate of change over the interval [7, 9] than the interval   [4, 6]?

x      f(x)

4     358

5      690

6     1178

7     1852

8     2742

9     3878

 

2.) What is (f+g)(x)?

 

f(x)= x3​ - x

 

g(x)=  x3+2x2-10

 

3.) 

What is (f⋅g)(x)?

 

f(x)=x2+2x−6

 

g(x)=x4+3

 Dec 21, 2018
 #1
avatar+5788 
+1

\(\bar{\Delta}_{[7,9]} = \dfrac{3878-1852}{9-7} = 1013\\ \bar{\Delta}_{[4,6]} = \dfrac{1178-358}{6-4}=410\\ \bar{\Delta}_{[7,9]}-\bar{\Delta}_{[4,6]} = 1013-410 = 603\)

 

\(f(x) = x^3-x\\ g(x) = x^3+2x^2-10\\ (f+g)(x) = f(x) + g(x) = 2x^3 +2x^2 - x - 10\)

 

\(f(x) = x^2+2x-6\\ g(x) = x^4+3\\ (f-g)(x) = f(x)-g(x) = -x^4+x^2+2x-9\)

.
 Dec 21, 2018
edited by Rom  Dec 21, 2018
 #2
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the third one was supposed to be f times g not minus.

thanks for your help though

Guest Dec 21, 2018
 #3
avatar+5788 
+1

\((f\cdot g)(x) = (x^2+2x-6)(x^4+3)\\ \text{I leave the multiplication to you}\)

Rom  Dec 21, 2018

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