Class 12

Math

Calculus

Application of Derivatives

Find the slope of the tangent to the curve $y=x_{3}−xatx=2$.

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Find the intervals in which the following functions are strictly increasing or decreasing: (a) $x_{2}+2x−5$(b) $10−6x−2x_{2}$(c) $−2x_{3}−9x_{2}−12x+1$(d) $6−9x−x_{2}$(e) $f(x)=(x+1)_{3}(x−3)_{3}$

For the curve $y=4x_{3}−2x_{5}$, find all the points at which the tangents passes through the origin.

Verify Lagranges's mean-value theorem for the following function:$f(x)=(sinx+cosx)$ on $[0,2π ]$

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

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

Verify Rolle's theorem for each of the following functions:$f(x)=1−x_{2} $ in $[−1,1]$

The approximate change in the volume of a cube of side $x$ metres caused by increasing the side by $3$% is :

The line $y=x+1$ is a tangent to the curve $y_{2}=4x$ at the point.