its asking to find the relative extrema ### Calculus Problems#### Problem 14**Function:**\[ f(x) = 2xe^{-x} \]**Note:**- The handwritten note suggests a relative maximum at a certain point: "rel max @."#### Problem 15**Task:** Find \( f''(x) \) for the function.**Function:**\[ f(x) = 2x^{3/2} - 6x^{1/2} \]**Solution:**The second derivative is calculated as:\[ f''(x) = \frac{3}{2}x^{-1/2} \]This image involves algebraic expressions and their derivatives, focusing on calculus concepts such as exponential functions and power rules.

Given: fx=2xe-x we know that at maxima derivative of given function has to be zero and derivative also change it's sign from positive to negative so, finding derivative of given function and equate it with zeroso, f'x=0ddx2xe-x=02ddxxe-x=0 ∵ ddxu.v=vdudx+udvdxe-xddxx+xddxe-x=0 ∵ ddxe-x=-e-x, ddxx=1e-x1+x-e-x=0e-x1-x=0-e-xx-1=0x=1 so, derivative of given function is zero at x=1 and it's changing sign from positive to negative for increasing x. hence, given function have maxima at x=1. The graph of the function is given by,

Answered: 14) f(x) = 2xe-X %3D

Math

Calculus

14) f(x) = 2xe-X %3D

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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