Class 12

Math

Calculus

Application of Derivatives

Find the absolute maximum and minimum values of the function f given by $f(x)=cos_{2}x+sinx,$$x∈[0,π]$

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Find the shortest distance of the point (0, c) from the parabola $y=x_{2}$, where $0≤c≤5$.

Find the approximate value of f(3.02), where $f(x)=3x_{2}+5x+3$.

Find the equations of all lines having slope 0 which are tangent to the curve $y=x_{2}−2x+31 $.

Find the equation of the tangent to the curve $y=(x−2(x−3)x−7 $ at the point where it cuts the x-axis.

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.

Use differential to approximate $36.6 $

Find the slope of the normal to the curve $x=1−asinθ,y=bcos_{2}θ$at $θ=2π $.

A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the maximum length of the hypotenuse is $(a_{32}+b_{32})_{23}$.