Class 12

Math

Calculus

Application of Derivatives

Prove that $y=(2+cosθ)4sinθ −θ$is an increasing function of $θ$in $[0,2π ]$.

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Find the possible values of $p$ such that the equation $px_{2}=(g)_{e}x$ has exactly one solution.

Find the minimum value of $(x_{1}−x_{2})_{2}+(20x_{1} −(17−x_{2})(x_{2}−13) )_{2}$ where $x_{1}∈R_{+},x_{2}∈(13,17)$.

Discuss the extremum of $f(x)=asecx+bcosecx,0<a<b$

Let $f(x)andg(x)$ be differentiable for $0≤x≤2$ such that $f(0)=2,g(0)=1,andf(2)=8.$ Let there exist a real number $c$ in $[0,2]$ such that $f_{prime}(c)=3g_{prime}(c)˙$ Then find the value of $g(2)˙$

Find the condition that the line $Ax+By=1$ may be normal to the curve $a_{n−1}y=x_{n}˙$

Discuss the extrema of $f(x)=1+xtanxx ,x∈(0,2π )$

The tangent to the parabola $y=x_{2}$ has been drawn so that the abscissa $x_{0}$ of the point of tangency belongs to the interval [1,2]. Find $x_{0}$ for which the triangle bounded by the tangent, the axis of ordinates, and the straight line $y=x02$ has the greatest area.

Find the locus of point on the curve $y_{2}=4a(x+as∈ax )$ where tangents are parallel to the axis of $x˙$