Question

F(x) = (x – 8)(x – 2)

Answer 1

So, f(x) has its roots at x = 2 and x = 8 and a minimum point at (5, -9)

How to find the roots of a function?

Since we are given the function f(x) = (x – 8)(x – 2), we are likely supposed to find the roots of the equation.

The roots of the function are obtained at the value of x for which f(x) = 0.

So, f(x) = 0

⇒ (x – 8)(x – 2) = 0

⇒ (x – 8) = 0 or (x – 2) = 0

⇒ x = 8 or x = 2

So, the roots of the function are x = 2 and x = 8.

The graph of f(x) crosses the x-axis at the roots of f(x) which are x = 2 and x = 8

Also, to find the maximum value of f(x), we differentiate with respect to x and equate to zero.

So, df(x)/dx = d(x - 8)(x - 2)/dx

= (x - 8) + (x - 2)

= 2x - 10

Equating to zero, we have

2x - 10 = 0

2x = 10

x = 10/2

x = 5

To determine if this is a maximum or minimum point,we differentiate f'(x)

So, df'(x)/dx = d(2x - 10)/dx = 2

Since f"(x) = 2 > 0, this is a minimum point.

So, the minimum point is f(5) = (5 - 8)(5 - 2) = (-3)(3) = -9

So, f(x) has its roots at x = 2 and x = 8 and a minimum point at  (5, -9)

Learn more about roots of a function here:

brainly.com/question/2833285

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