Class 12

Math

Calculus

Application of Derivatives

) Find the intervals in which the function $sin3x,x∈[0,2π ]$, is (a) increasing (b) decreasing

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Show that $f(x)=x(x−5)_{2}$ satisfies Rolle's theorem on $[0,5]$ and that the value of $c$ is $(35 )$

Find the slope of the tangent to the curve $y=x_{3}−3x+2$ at the point whose $x$ coordinate is $3$.

Prove that the function given by $f(x)=x_{3}−3x_{2}+3x−100$ is increasing in $R$.

The total revenue in Rupees received from the sale of $x$ units of a product is given by $R(x)=3x_{2}+36x+5$. The marginal revenue, when $x=15$ is.

Using differentials, find the sum of digits approximate value of the following up to $3$ places of decimal.$(82)_{41}$

Find the slope of the tangent to the curve $y=3x_{4}−4x$ at x = 4.

Using differentials, find the approximate value of :$329 $

Find the slope of the tangent to the curve $y=x−2x−1 ,x=2$ at $x=10.$