class 12

Math

Calculus

Application of Derivatives

The number of points in $(−∞,∞),$for which $x_{2}−xsinx−cosx=0,$is6 (b) 4 (c) 2 (d) 0

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If the function $y=f(x)$ is represented as $x=ϕ(t)=t_{5}−5t_{3}−20t+7$, $y=ψ(t)=4t_{3}−3t_{2}−18t+3(∣t∣<2),$ then find the maximum and minimum values of $y=f(x)˙$

Find the values of $p$ if $f(x)=cosx−2px$ is invertible.

Find the equation of the normal to the curve $x_{3}+y_{3}=8xy$ at the point where it meets the curve $y_{2}=4x$ other than the origin.

Is every invertible function monotonic?

A figure is bounded by the curves $y=x_{2}+1,y=0,x=0,andx=1.$ At what point $(a,b)$ should a tangent be drawn to curve $y=x_{2}+1$ for it to cut off a trapezium of greatest area from the figure?

Discuss the extremum of $f(x)={1+sinx,x<0x_{2}−x+1,x≥0atx=0$

Two cyclists start from the junction of two perpendicular roads, there velocities being $3um/m∈$ and $4um/m∈$ , respectively. Find the rate at which the two cyclists separate.

Find the length of normal to the curve $x=a(θ+sinθ),y=a(1−cosθ)$ at $θ=2π ˙$