Let a function f(x) be continuous in an interval [a, b]. Let \delta > 0 be a very small real number. Let {c} \in(a, b) be such that f( {c}-\delta) < f( {c}) and f( {c}+\delta) < f( {c}) for every \delta>0. Let (f(\alpha-\delta)-f(\alpha))(f(\alpha+\delta)-f(\alpha))< 0 \forall \alpha \in(a, b) and \alpha \neq {c}. Then

Correct Answer is : f(x) has only one local maximum at c

f(x) has a local maximum at {c} and a local minimum at \alpha

f(x) has a local maximum at \alpha and a local minimum at {c}

f(x) has only one local maximum at {c}

f(x) has only one local minimum at c

TS EAMCET 18-July-2022 Shift 1 Solved Paper

Section: Mathematics

Question : 72 of 160

Marks: +1, -0

Let a function f(x) be continuous in an interval [a,b]. Let δ>0 be a very small real number. Let c∈(a,b) be such that f(c−δ)<f(c) and f(c+δ)<f(c) for every δ>0. Let (f(α−δ)−f(α))(f(α+δ)−f(α))<0‌‌∀α∈(a,b) and α≠c. Then

f(x) has a local maximum at c and a local minimum at α
f(x) has a local maximum at α and a local minimum at c
f(x) has only one local maximum at c
f(x) has only one local minimum at c

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