class 12

Math

Calculus

Application of Derivatives

For $x∈(0,25π )$, define $f(x)=∫_{0}t sintdt$Then f has : local maximum at $π$ and $2π$ . local minimum at $π$ and $2π$ local minimum at $π$ and local maximum at $2π$ . local maximum at $π$ and local minimum at $2π$ .

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

Find the intervals in which the function $f$ given $f(x)=s∈x+cosx,0≤x≤2π,$ is strictly increasing or strictly decreasing.

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

A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at the rate of 0.05 cm/s. Find the rate at which its area is increasing when radius is 3.2 cm.

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

Find the maximum and minimum values, if any, of the following functions given by(i) $f(x)=∣x+2∣−1$ (ii) $g(x)=−∣x+1∣+3$ (iii) $h(x)=sin(2x)+5$ (iv) $f(x)=∣sin4x+3∣$

Prove that the following functions do not have maxima or minima:(i) f (x) = $e_{x}$ (ii) $g(x)=gx$(iii) $h(x)=x_{3}+x_{2}+x+1$

Find the maximum and minimum values of f , if any, of the function given by $f(x)=∣x∣,x∈R$.