Class 12

Math

Calculus

Application of Derivatives

Find the equations of the tangent and normal to the parabola $y_{2}=4ax$at the point $(at_{2},2at)$.

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Draw the graph of $f(x)=x_{2}−xx_{2}−5x+6 $

If $fogoh(x)$ is an increasing function, then which of the following is not possible? (a)$f(x),g(x),andh(x)$ are increasing (b)$f(x)andg(x)$ are decreasing and $h(x)$ is increasing (c)$f(x),g(x),andh(x)$ are decreasing

Does there exists line/lines which is/are tangent to the curve $y=sinxat(x_{1},y_{1})$ and normal to the curve at $(x_{2},y_{2})?$

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

Find the values of $a$ if equation $1−cosx=23 ∣x∣+a,x∈(0,π),$ has exactly one solution.

If the curve $C$ in the $xy$ plane has the equation $x_{2}+xy+y_{2}=1,$ then the fourth power of the greatest distance of a point on $C$ from the origin is___.

If the radius of a sphere is measured as 9cm with an error of 0.03 cm, then find the approximate error in calculating its volume.

Find the normal to the curve $x=a(1+cosθ),y=asinθahη˙$ Prove that it always passes through a fixed point and find that fixed point.