the function g(x) Is the graph below resulted from shifting the graph of f(x) down 2 units. If f’(2)=8, what is g’(2)?

Mathematics

1 answer:

Sauron [17]1 year ago

4 0

We know that the graph of g(x) is the result of a shift of 2 units down from f(x).

Then, f(x) and g(x) are related by:

$g(x)=f(x)-2$

Taking the derivative:

$g^{\prime}(x)=f^{\prime}(x)$

This is because the derivative of a constant number is 0. Finally, evaluating at x = 2:

$\begin{gathered} g^{\prime}(2)=f^{\prime}(2) \\ \\ \therefore g^{\prime}(2)=8 \end{gathered}$

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3 years ago

What is the y-intercept of the quadratic function f(x) = (x – 8)(x + 3)? (8,0) (0,3) (0,–24) (–5,0)

DiKsa [7]

The correct answer is: [C]: " (0, 24) " .
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Explanation:
___________________________________________________________

Given the quadratic function:
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→ " y = (x − 8) (x + 3) " ; ← Note: Replace the "f(x)" with: "y" ;

→ Find the "y-intercept".
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→ Note: The "y-intercept" is the coordinate of the point(s) of the graph of the equation at which the graph crosses the "x-axis" when "x = 0" .

→ So; we set plug in "0" for "x" into our equation; and solve for "y" ;

 → " y = (x − 8) (x + 3) " ;

 → y = (0 − 8) (0 + 3) ;

 → y = (-8) * (3) ;

 → y = - 24 ;
___________________________________________________________

So, the "y -intercept" of the given quadratic function is:

the point at which: "x = 0 ; y = -24 " ;

→ that is; the point the coordinates: " (0, - 24) " ;
___________________________________________________________
→ which is: Answer choice: [C]: " (0, - 24) " .
___________________________________________________________

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3 years ago

Read 2 more answers

Which graph represents the solution set for the system 6x + y > -3 and 2x + y ≤ 4?

VikaD [51]

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The doubly-shaded area is the solution set. The dashed line is not included.