Chapter 4: Q21MP (page 239)

Find the hottest and the coldest point on the bar graph of 5. If $T = 4 x - x^{2}$ , where x is distance measured from the left end.

Short Answer

Expert verified

The hottest and the coldest point on the bar graph are $2$ and $5$ .

Step by step solution

Given information

Given that . $T = 4 x - x^{2}$

Find the critical points

Differentiate the function with respect to $x$ .

4-2x

Substitute $\frac{d T}{d x} = 0$ .

$4 - 2 x = 0 2 x = 4 x = 2$

Find the relative maximum

Differentiate the function $\frac{d T}{d x}$ with respect to $x$ .

Since $\frac{d^{2} T}{d x^{2}} = - 2 < 0$ so the function has the relative maximum at $x = 2$ .

Find the value of the function

The value of the function $T$ at $x = 0, 2, 5$ .

$T (0) = 4 \times 0 - {(0)}^{2} = 0 - 0 = 0$

$T (2) = 4 \times 2 - {(2)}^{2} = 8 - 4 = 4$

$T (5) = 4 \times 5 - {(5)}^{2} = 20 - 25 = - 5$

The absolute maximum value is 4 at $x = 2$ and the absolute minimum value is -5 at $x = - 5$ .

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Find the hottest and the coldest point on the bar graph of 5. If $T = 4 x - x^{2}$ , where x is distance measured from the left end.

Short Answer

Step by step solution

Given information

Find the critical points

Find the relative maximum

Find the value of the function

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Find the hottest and the coldest point on the bar graph of 5. If T=4x-x2, where x is distance measured from the left end.

Short Answer

Step by step solution

Given information

Find the critical points

Find the relative maximum

Find the value of the function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electromagnetism

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Find the hottest and the coldest point on the bar graph of 5. If $T = 4 x - x^{2}$ , where x is distance measured from the left end.