Class 12

Math

Calculus

Application of Derivatives

Find the maximum and the minimum values, if any, of the function f given by$f(x)=x_{2},x∈R$.

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Find the equations of the normal to the curve $y=x_{3}+2x+6$ which are parallel to the line $x+14y+4=0.$

Using Lagranges mean value theorem, prove that $∣cosa−cosb∣≤∣a−b∣˙$

Points on the curve $f(x)=1−x_{2}x $ where the tangent is inclined at an angle of $4π $ to the x-axis are (0,0) (b) $(3 ,−23 )$ $(−2,32 )$ (d) $(−3 ,23 )$

Let $x$ be the length of one of the equal sides of an isosceles triangle, and let $θ$ be the angle between them. If $x$ is increasing at the rate (1/12) m/h, and $θ$ is increasing at the rate of $180π $ radius/h, then find the rate in $m_{3}$ / $h$ at which the area of the triangle is increasing when $x=12mandthη=π/4.$

Discuss the extremum of $f(x)=31 (x+x1 )$

Find the range of the function $f(x)=(x_{2}+1)_{2}x_{4}+x_{2}+5 $

Discuss the extremum of $f(x)=2x+3x_{32}$

The latest edge of a regular hexagonal pyramid is $1cm˙$ If the volume is maximum, then find its height.