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Kitty [74]
1 year ago
5

Question is in the image. I need help with #19

Mathematics
1 answer:
Naddika [18.5K]1 year ago
6 0

EXPLANATION

Replacing the given functions into the following:

\frac{f(x+h)-f(x)}{h}\frac{x^2-1+h-(x^2-1)}{h}

Removing the parentheses and simplifying:

\frac{x^2-1+h-x^2+1}{h}

Simplifying like terms:

\frac{h}{h}=1

Hence,

\frac{f(x+h)-f(x)}{h}=1

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For what value of x will the function f(x) = -3(x - 10)(x - 4) have a maximum value? Find the maximum value.
gayaneshka [121]

Hello!

To find the maximum value of the function f(x) = -3(x - 10)(x - 4), the easiest way is to find the vertex using the formula: x = -b/2a.

Firstly, we need to simplify f(x).

f(x) = -3(x - 10)(x - 4)

f(x) = -3(x² - 14x + 40)

f(x) = -3x² + 42x + -120

Since the equation f(x) is now simplified to standard form, we can find the vertex.

a = -3, b = 42, and c = -120

x = -(42)/2(-3) = -42/-6 = 7

Then, we substitute 7 into the the function f(x) = -3(x - 10)(x - 4), or

f(x) = -3x² + 42x + -120, to find the y-value of the vertex.

f(x) = -3(7 - 10)(7 - 4)

f(x) = -3(-3)(4)

f(x) = 27

The vertex of f(x) is (7, 27).

Therefore, the maximum x-value for the function f(x) is 7.

4 0
3 years ago
Read 2 more answers
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