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NCERT Class 12 Maths Chapter 6: Applications Of Derivatives 16 Questions Solved

NCERT Solutions for Class 12 Maths Chapter 6 Applications Of Derivatives — Miscellaneous Exercise

Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.

Show f(x)=log x/x has its maximum at x=e.

The equal sides of an isosceles triangle with fixed base b shrink at 3 cm/s. Find the area-decrease rate when each equal side equals b.

Find increasing/decreasing intervals of f(x)=(4sin x−2x−x cos x)/(2+cos x).

Find increasing/decreasing intervals of x³+1/x³, x≠0.

Find the maximum area of an isosceles triangle inscribed in x²/a²+y²/b²=1, vertex at an end of the major axis.

An open rectangular tank has depth 2 m, volume 8 m³. Base costs ₹70/m² and sides ₹45/m². Find minimum construction cost.

If circle circumference plus square perimeter is k, prove the area sum is least when square side equals circle diameter.

A window is a rectangle surmounted by a semicircle. Its perimeter is 10 m. Find dimensions admitting maximum light.

A point on the hypotenuse of a right triangle has perpendicular distances a,b>0 from its legs. Show the least hypotenuse length is…

For f(x)=(x−2)⁴(x+1)³ find (i) local maxima, (ii) local minima, (iii) points of inflexion.

Find absolute extrema of cos²x+sin x on [0,π].

Show the maximum-volume cone inscribed in a sphere of radius R has altitude 4R/3.

Let f be defined on [a,b], with f′(x)>0 for every x∈(a,b). Prove f increases on (a,b).

Find the height and volume of the maximum-volume cylinder inscribed in a sphere of radius R.

A cylinder is inscribed coaxially in a right circular cone of height H and semi-vertical angle α. Show its maximum-volume height is…

A cylindrical tank of radius 10 m receives wheat at 314 m³/h. Find the depth rate.