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Question

# For the shown graph the slope of graph from point A to point B:

A
Continuously decreases
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B
Continuously increases
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C
First increases then decreases
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D
First decreases then increases
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Solution

## The correct option is A Continuously decreases(A)Slope of the graph = tangent of angle made by tangent with +x axisFrom A→C : θ is acute and decreases ⇒ slope decreaseFrom C→B : θ is obtuse and decreases ⇒ slope decreasesExplanation of variation: Let s=tanθds=sec2θdθsince sec2θ≥0(non negative)so dθ decides sign of dsand since dθ is negative in both case ⇒ds is negativeso slope decreases continously

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