# Answer the following questions for the functionf(x) = xVx² + 25defined on the interval [-7,5].A.f(x) is concave down on the regiontoB.f(x) is concave up on the regionC. The inflection point for this function is attoD. The minimum for this function occurs atE. The maximum for this function occurs at

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6 views help_outlineImage TranscriptioncloseAnswer 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 fullscreen
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Step 1 help_outlineImage TranscriptioncloseThe 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)? fullscreen
Step 2

Equate the second derivative to zero to find the critical point. help_outlineImage Transcriptionclose2x + 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- fullscreen
Step 3

Sketch the graph of the functio... help_outlineImage Transcriptionclose(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 fullscreen

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