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Mumz [18]
3 years ago
13

What is the maximum number of possible extreme values for the function, f(x) = х2 -7x – 6?

Mathematics
1 answer:
timama [110]3 years ago
3 0

Answer:

Only one extreme value of f(x) is possible.

Step-by-step explanation:

We are given the quadratic function of independent variable x which is f(x) = x² - 7x - 6 ......(1)

Now. the condition for extreme values of f(x) is \frac{df(x)}{dx} =0

Hence, differentiating both sides of equation (1) with respect to x, we get

\frac{df(x)}{dx} = 2x -7 = 0

⇒ x = 3.5.

So there is only one value of x for which f(x) has extreme value which is x = 3.5.

Therefore, only one extreme value of the given function is possible. (Answer)

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\begin{array}{rcl}\\\left \{ & = & \text{The set of}\\x & = & \text{all x values}\\| & = &\text{such that}\\x & = & x\\\in & = &\text{is a member of}\\\mathbb{R}, & = &\text{all real numbers, and}\\x < -2 & = & \text{x is less than -2}\\\end{array}\\\text{The answer is }\boxed{\textbf{A. }\mathbf{\left \{ x \, | \, x \in \mathbb{R}, x < -2 \right \} }}}

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