Question 76 of 82intermediate🔧 ApplyLong Answer5 marks

Find the points at which the function ff given by f(x)=(x−2)4(x+1)3f(x) = (x - 2)^4 (x + 1)^3 has

(i)

local maxima

Answer

x = 2/7 is a point of local maxima

(ii)

local minima

Answer

x = 2 is a point of local minima

(iii)

point of inflexion

Answer

x = -1 is a point of inflexion

Explanation

This problem requires finding critical points by setting f′(x)=0f'(x) = 0 and then applying the first derivative test to classify each point. The multiplicity of factors in the derivative determines whether the sign changes at each critical point.

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