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UPSC NDA I 2021 Mathematics Solved Paper

Question : 97 of 120

Marks: +1, -0

The curve

y=-x^{3}+3x^{2}+2x-27

Solution: 👈: Video Solution

Concept:

Slope of a curve

y=f(x)

at a point is the value of its first derivative at that point.

i.e.

m=f(x)

Calculation:

The slope of the curve

y=-x^{3}+3x^{2}+2x-27

will be given by:

m=y'\;\frac{d}{dx}(-x^{3}+3x^{2}+2x-27)=-3x^{2}+6x+2

In order to maximize the slope, we must have

m'=0

and

m''<0

. Now,

m'=0

\Rightarrow \;\frac{d}{dx}(-3x^{2}+6x+2)=-6x+6=0

\Rightarrow x=1

And

m''=-6<0

Therefore, the slope is maximum at

x=1

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