Application of Derivatives
The tangent to the curve y=ex drawn at the point (c,ec) intersects the line joining (c−1,ec−1)and(c+1,ec+1) (a) on the left of n=c (b) on the right of n=c (c) at no points (d) at all points
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Find the intervals in which the function f given by f(x)=x2−4x+6is (a) strictly increasing (b) strictly decreasing
) Find the intervals in which the function sin3x,x∈[0,2π], is (a) increasing (b) decreasing
Find the equation of all lines having slope 1that are tangents to the curve y=x−11,x=1.
The line y=x+1is a tangent to the curve y2=4xat the point(A) (1,2) (B)(2,1) (C) (1,2) (D) (1,2)
Find the maximum and the minimum values, if any, of the function f given byf(x)=x2,x∈R.
Find the slope of the tangent to the curve y=x−2x−1,x=2 at x=10.
Find the equation of the normal to curve x2=4ywhich passes through the point (1, 2).
Find the points on the curve y=x3at which the slope of the tangent is equal to the y-coordinate of the point.