Class 12

Math

Calculus

Application of Derivatives

Find the equation of the normal at the point $(am_{2},am_{3})$for the curve $ay_{2}=x_{3}$.

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Show that the function given by $f(x)=e_{2x}$ is strictly increasing on $R$.

Verify Rolle's theorem for each of the following functions:$f(x)=x_{3}−7x_{2}+16x−12$ in $[2,3]$

Verify Rolle's theorem for each of the following functions:$f(x)=sin3x$ in $[0,π]$

Find the maximum and minimum values of $3x_{4}−8x_{3}+12x_{2}−48x+1$ on the interval $[1,4]$

Using differentials, find the approximate value of :$(2.002)_{2}1 $

Verify Rolle's theorem for each of the following functions:$f(x)=x(x+2)e_{x}$ in $[−2,0]$

The interval in which $y=x_{2}e_{x}$ is decreasing is.

The radius of a circle is increasing at the rate of $0.7cm/s$. What is the rate of increases of its circumference ?