1. Find the slope of the tangent to the curve y = 3x4 4x at x = 4. 2. Find the slope of the tangent to the curve 1 , 2 2 x y x x = at x = 10. 3. Find the slope of the tangent to curve y = x3 x + 1 at the point whose x-coordinate is 2. 4. Find the slope of the tangent to the curve y = x3 3x + 2 at the point whose x-coordinate is 3. 5. Find the slope of the normal to the curve 3 3 x = acos q, y = asin q at . 4 p q = 6. Find the slope of the normal to the curve 2 x = 1 asinq, y = bcos q at . 2 p q = 7. Find points at which the tangent to the curve y = x3 3x2 9x + 7 is parallel to the x-axis. 8. Find a point on the curve y = (x 2)2 at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4). 10. Find the equation of all lines having slope 1 that are tangents to t
Question 1:Find the slope of the tangent to the curve y = 3x4 – 4x at x = 4.
Question 2:Find the slope of the tangent to the curve 1 , 2 2 x y x x − = ¹ − at x = 10.
Question 3:Find the slope of the tangent to curve y = x3 – x + 1 at the point whose x-coordinate is 2.
Question 4:Find the slope of the tangent to the curve y = x3 –3x + 2 at the point whose x-coordinate is 3.
Question 5:Find the slope of the normal to the curve 3 3 x = acos q, y = asin q at . 4 p q =
Question 6:Find the slope of the normal to the curve 2 x = 1− asinq, y = bcos q at . 2 p q =
Question 7:Find points at which the tangent to the curve y = x3 – 3x2 – 9x + 7 is parallel to the x-axis.
Question 8:Find a point on the curve y = (x – 2)2 at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).
Question 10:Find the equation of all lines having slope –1 that are tangents to the curve 1 1 y x = − , x ¹ 1.
Question 11:Find the equation of all lines having slope 2 which are tangents to the curve 1 3 y x = − , x ¹ 3.
Question 12:Find the equations of all lines having slope 0 which are tangent to the curve 2 1 . 2 3 y x x = − +
Question 13:Find points on the curve 2 2 1 9 16 x y + = at which the tangents are (i) parallel to x-axis (ii) parallel to y-axis.
Question 14:Find the equations of the tangent and normal to the given curves at the indicated points: (i) y = x4 – 6x3 + 13x2 – 10x + 5 at (0, 5) (ii) y = x4 – 6x3 + 13x2 – 10x + 5 at (1, 3) (iii) y = x3 at (1, 1) (iv) y = x2 at (0, 0) (v) x = cos t, y = sint at 4 t p =
Question 15:Find the equation of the tangent line to the curve y = x2 – 2x +7 which is (a) parallel to the line 2x – y + 9 = 0 (b) perpendicular to the line 5y – 15x = 13.
Question 16:Show that the tangents to the curve y = 7x3 + 11 at the points where x = 2 and x = – 2 are parallel.
Question 17:Find the points on the curve y = x3 at which the slope of the tangent is equal to the y-coordinate of the point.
Question 18:For the curve y = 4x3 – 2x5, find all the points at which the tangent passes through the origin.
Question 19:Find the points on the curve x2 + y2 – 2x – 3 = 0 at which the tangents are parallel to the x-axis.
Question 20:Find the equation of the normal at the point (am2,am3) for the curve ay2 = x3.
Question 21:Find the equation of the normals to the curve y = x3 + 2x + 6 which are parallel to the line x + 14y + 4 = 0.
Question 22:Find the equations of the tangent and normal to the parabola y2 = 4ax at the point (at2, 2at).
Question 23:Prove that the curves x = y2 and xy = k cut at right angles* if 8k2 = 1.
Question 24:Find the equations of the tangent and normal to the hyperbola 2 2 2 2 1 x y a b − = at the point (x0, y0).
Question 25:Find the equation of the tangent to the curve y = 3x − 2 which is parallel to the line 4x − 2y + 5 = 0 . Choose the correct answer in Exercises 26 and 27
Question 26:The slope of the normal to the curve y = 2x2 + 3 sin x at x = 0 is (A) 3 (B) 1 3 (C) –3 (D) 1 3 −
Question 27:The line y = x + 1 is a tangent to the curve y2 = 4x at the point (A) (1, 2) (B) (2, 1) (C) (1, – 2) (D) (– 1, 2)
