Let f:R→Rbe a differentiable and increasing function ∀x∈R. If the tangent drawn to the curve at any point x∈(a$$,$$b) always lies below the curve, then

Clearly , for f′(x)>$$0$$,f′′(x)>$$0$$ [in Figure (c)], tangent always lies below the graph. For f′(x) $$0$$ [in Figure (d)], tangent always lies below the graph.

Let f:R→Rbe a differentiable and increasing function ∀x∈R. If the tangent drawn to the curve at any point x∈(a$$,$$b) always lies below the curve, then

Correct option is 3f′(x)>0,f′′(x)>0∀x∈(a,b)

Questions

Let $f : R \to R$ be a differentiable and increasing function $\forall x \in R$ . If the tangent drawn to the curve at any point $x \in (a, b)$ always lies below the curve, then

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f′(x)>0,f′′(x)<0∀x∈(a,b)

f′(x)<0,f′′(x)<0∀x∈(a,b)

f′(x)>0,f′′(x)>0∀x∈(a,b)

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detailed solution

Correct option is C

Clearly , for f′(x)>0,f′′(x)>0 [in Figure (c)], tangent always lies below the graph. For f′(x)<0,f′′(x)>0 [in Figure (d)], tangent always lies below the graph.

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