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grin007 [14]
2 years ago
8

Please please help *image attached* it’s ap calc ab

Mathematics
1 answer:
vaieri [72.5K]2 years ago
8 0

The average rate of change of a function f(x) over some interval [a, b] is the difference quotient,

\dfrac{f(b)-f(a)}{b-a}

which corresponds to the slope of the line connecting the points (a, f(a)) and (b, f(b)) in the graph of f(x).

Given f(x) = 3x² - x³ (correct me if I'm wrong, the exponents look cut off in your screenshot), the average rate of change on [1, 5] is

\dfrac{f(5)-f(1)}{5-1}=\dfrac{(3\cdot5^2-5^3)-(3\cdot1^2-1^3)}4 = \dfrac{75-125-3+1}4 = \boxed{-13}

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I need help with 11 and 12
Yakvenalex [24]

Answer:

Both are inverse pairs  

Step-by-step explanation:

Question 11

g(x)= 4 + \dfrac{8}{5}x

(a) Rename g(x) as y  

y = 4 + \dfrac{8}{5}x

(b) Solve for x :  

\dfrac{8}{5}x = y - 4

(c) Multiply each side by ⅝

x = \dfrac{5}{8}(y - 4) = \dfrac{5}{8}y - \dfrac{5}{2}

(d) Switch x and y  

y = \dfrac{5}{8}x - \dfrac{5}{2}

(e) Rename y as the inverse function  

g^{-1}(x) = \dfrac{5}{8}x - \dfrac{5}{2}

(f) Compare with your function

f(x) = \dfrac{5}{8}x - \dfrac{5}{2}\\\\f(x) = g^{-1}(x)

f(x) and g(x) are inverse functions.

The graphs of inverse functions are reflections of each other across the line y = x.

In the first diagram, the graph of ƒ(x) (blue) is the reflection of g(x) (red) about the line y = x (black)

 

Question 12

h(x)= x - 2

(a) Rename h(x) as y  

y = x - 2

(b) Solve for x:  

x = y + 2

(c) Switch x and y  

y  = x + 2

(e) Rename y as the inverse function  

h⁻¹(x) = x + 2

(f) Compare with your function

f(x) = x + 2

f(x) = h⁻¹(x)

h(x) and ƒ(x) are inverse functions.

The graph of h(x) (blue) reflects ƒ(x) (red) across the line y = x (black).

5 0
2 years ago
Find the slope of the following equation .simplify your answer 5x+2y=-10
defon

Answer:

m=-5/2

Step-by-step explanation:

Use the slope-intercept form y=mx+b to find the slope m.

6 0
2 years ago
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Lapatulllka [165]
Hello there!

We can use the following expression:

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~DL
5 0
2 years ago
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Answer:

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Step-by-step explanation:

Given:

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