Application of Derivatives
If f(x)∣cos(2x)cos(2x)sin(2x)−cosxcosx−sinxsinxsinxcosx∣,then:fprime(x)=0at exactly three point in (−π,π)fprime(x)=0at more than three point in (−π,π)f(x)attains its maximum at x=0f(x)attains its minimum at x=0
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The maximum value of [x(x−1)+1]31,0≤x≤1is(A) (31)31 (B) 21 (C) 1 (D) 0
Find all the points of local maxima and local minima of the function f given by f(x)=2x3−6x2+6x+5.
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 approximate value of f(3.02), where f(x)=3x2+5x+3.
Find the intervals in which the function f
given f(x)= s∈x+cosx, 0≤x ≤2π,
is strictly increasing or strictly decreasing.
Find the slope of the tangent to the curve y=x3−3x+2 at the point whose x-coordinate is 3.
The normal to the curve x2=4ypassing (1,2) is(A) x+y=3 (B) xy=3 (C) x+y=1 (D) xy=1
The interval in which y=x2e−xis increasing is(A) (−∞,∞) (B) ( 2, 0) (C) (2,∞) (D) (0, 2)