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x C Chegg Study /Guided Solutio x C S Sign In or Sign Up | Chegg.cor X 18/ONL #Student&enroll-UIUC;/NetMath/Math nthropology103 Q Your Sets I Quizlet MATH 220 ONL Pla..Mathable CALC220 Back to Dashboard Help Bryena Rivera( View Original C Cell Evaluation 1.e.?) Calculus Cal You look up from your machine and see the dreaded computer pest Calculus Cal sit down next to you. Cal says: "If I have a function fx] and I know that f'la] -0 then I know that the plot of f[x] has a crest or a dip at (a, flal) You say, "Cal, you are mistaken Look at this plot of x, inthe vicinity of x-0 :" Clearlf, xl: f(x_1 = x^3 ; AxesLabel Plot [f(x),1(x?-0.5, 0.5), PlotRange-> All, plotstyle-> {Thickness(0.01), Orange)), ("x", "fIx]")1 0.10 0.05 0.4 0.2 0.4 -0.05 Q10 Now you take over and tell Cal why this example shows that Cal is wrong Comment on these statements: l)lfria)-0 .then the plot of fIx] is guaranteed to have a crest or a dip at [a.flal 2) It the plot of fl] has a crest or dip at (a, fla then it is automatic that r'ia)-o

Explanation / Answer

ansswer to 1.e.iii) is false

both the statements are different

statement 1) is not always true. a counter example is given above y= x^3

but the statement 2) is always true because if a function has crest or dip at any point it automatically means that is derivate will be zero at that point( the only condition is that the given function must be differentiable at those points)

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