Find the point on the curve y = x³ – 11x + 5 at which the equation of tangent is y = x – 11.
Find the points on the curve y = x³ – 3x² – 9x + 7 at which the tangent to the curve is parallel to the x-axis.
Find the points on the curve x² + y² – 2x – 3 = 0 at which tangent is parallel to x-axis.
Find the slope of tangent to the curve y = 3x² – 6 at the point on it whose x-coordinate is 2.
Find the equations of the normal to the curve x² = 4y which passes through the point (1, 2).
Show that a function f : R → R given by f(x) =ax + b,a, b ∈ R, a ≠ 0 is a bijective.
Find the equations of tangents to the curve y = (x²– 1) (x – 2) at the points, where the curve cuts the X-axis.
Two farmers X and Y cultivate only three varieties of rice namely Basmati, Permal and Naura. The sale in rupees of these varieties of rice by both the farmers in the months of September and October are given by the following matrices A and B.
In a parliament election, a political party hired a public relations firm to promote its candidates in three ways — telephone, house calls and letters. The cost per contact (in paise) is given in matrix A as
Find the particular solution of the following differential equation :