Application of Derivatives
Find the absolute maximum and minimum values of the function f given by f(x)=cos2x+sinx,x∈[0,π]
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Find the shortest distance of the point (0, c) from the parabola y=x2, where 0≤c≤5.
Find the approximate value of f(3.02), where f(x)=3x2+5x+3.
Find the equations of all lines having slope 0 which are tangent to the curve y=x2−2x+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=bcos2θat 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 (a32+b32)23.