Question
Asked Dec 6, 2019
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Answer the following questions for the function
f(x) = xVx² + 25
defined on the interval [-7,5].
A.f(x) is concave down on the region
to
B.f(x) is concave up on the region
C. The inflection point for this function is at
to
D. The minimum for this function occurs at
E. The maximum for this function occurs at
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Answer the following questions for the function f(x) = xVx² + 25 defined on the interval [-7,5]. A.f(x) is concave down on the region to B.f(x) is concave up on the region C. The inflection point for this function is at to D. The minimum for this function occurs at E. The maximum for this function occurs at

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Expert Answer

Step 1
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The given function is f(x)=xvx² + 25 and the interval is [-7,5]. Find the second derivative of the given function. f(x) = (xVx* + 25 xyx + 25 dx %3D 2x + 25 (x² + 25)? 2x + 25 f"(x) = dx (x² + 25)? 2x + 75x (x² + 25)?

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Step 2

Equate the second derivative to zero to find the critical point.

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2x + 75x %3D 0 = (x² +25)? 2x + 75x = 0 x = 0, 2x² + 75 = 0 x = 0, x = ±i- the only inflection point is x = 0. 2 Ignore the imaginary root x=±i-

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Step 3

Sketch the graph of the functio...

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(5,35.36), 30- 20- Inflection point 10+ -4 -3 -2 -10 1 2 -7 -6 -5 4 -10+ y =xVx? + 25 -20+ -30- -40+ -50+ {(-7,-60.22) -60+ -70 15

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