Class 12

Math

Calculus

Application of Derivatives

Find the points at which the function f given by $f(x)=(x−2)_{4}(x+1)_{3}$has(i) local maxima (ii) local minima (iii) point of inflexion

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Find the absolute maximum and minimum values of a function f given by $f(x)=2x_{3}−15x_{2}+36x+1$on the interval $(3.02),$$[1,5]$.

Prove that the function f given by $f(x)=gcosx$ is strictly decreasing on $(0,2π )$and strictly increasing on $(2π ,π)$

Find the equation of the tangent to the curve $y=(x−2(x−3)x−7 $ at the point where it cuts the x-axis.

Find the equation of all lines having slope 2 and being tangent to the curve $y+x−32 =0$.

Prove that the function given by $f(x)=x_{3}−3x_{2}+3x−100$is increasing in R.

If length of three sides of a trapezium other than base are equal to 10cm, then find the area of the trapezium when it is maximum.

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

The normal at the point (1,1) on the curve $2y+x_{2}=3$is(A) $x+y=0$ (B) $xy=0$ (C) $x+y+1=0$(D) $xy=0$