Class XII ISC Chapter Application Of Derivatives
Explore our extensive collection of Application of Derivatives questions, tailored for class 12 students following the ISC curriculum. This topic is vital for understanding how to optimize a particular outcome given certain constraints. Our practice questions cover various aspects of Linear Programming, including formulating linear inequalities, graphical methods, and finding optimal solutions. Whether you're looking to strengthen your problem-solving skills or prepare for your exams, these questions provide the perfect resource to master Application of Derivatives concepts with ease.
class 12 A.O.D exercise7-1
Application of Derivatives
Select Exercise
Question 1
Q(ii)
What is the slope of the tangent to the following curves where y=3x4 - 4x at x=4
Q(iii)
What is the slope of the tangent to the following curves where x2+3y+y2=5 at the point (1, 1)
Q(iv)
What is the slope of the tangent to the following curves where y= x3-3x+2 at the point whose x-coordinate is 3
Q(v)
What is the slope of the tangent to the following curves where y= 3x2+4x at the point whose x-coordinate is -2
Question 2
Q(i)
What is the slope of the normal to the following curves where y= x3-5x2-x+1 at the point (1, -4)
Q(ii)
What is the slope of the normal to the following curves where y= 2x2+3 sinx at x = 0
Q4
Determine the point on the curve y = 3x2 -1 at which the slope of the tangent is 3.
Q5
At what point on the curve y = x2 does the tangent make an angle of 45° with the x-axis
Q8
Find the slopes of the tangents at the three points where the curve
y=x(x2-3x-4) cuts the x-axis
Q9
Show that the tangents to the curve y = 7x3 + 11 at the points where x =2 and x=-2 are parallel
Q10
If the tangent to the curve y = x3+ax +b at (1, -6) is parallel to the line 2x-2y+7=0,find a and b
Q11
Determine the point of the curve y = 3x2-5 at which the tangent is perpendicular to a line whose slope is -1/3
Q12(i)
Determine the points on the curve y = x3 - 3x2 - 9x + 7 at which the parallel tangents are to x-axis
Q12(ii)
Find the points on the curve x2+y2-2x -3 = 0 at which the tangents are parallel to x-axis
Q12(iii)
Find the points on the curve x2 / 4 + y2 / 25 =1 at which the tangents are
- parallel to x-axis
- parallel to y-axis
Q13(i)
Find the points on the curver x2 + y2 = 13, the tangent at each one of which is parallel to the line 2x 3y = 7
Q13(ii)
Find the points on the curver y=x3 - 3x2+2x, at which the tangent lines are parallel to the line y - 2x + 3 = 0.
Q14
Find the equations of the tangent and the normal to each of the following curves at the given point
Q16(i)
Find the equation of the tangent to the curve √x +√y =a at the point ( a2 / 4 , a2 / 4 )
Q16(ii)
Find the equations of the tangent and the normal to the curve
x2/3 +y2/3 =2 at (1,1)
Q17(i)
Find the equation of tangent to ihe curve given by x=asin3t ,y=bcos3t at a point where t=π/2
Q18
Find the equations of all lines having slope 2 and that are tangents to the curve y= 1 / x-3
Q19(i)
Find the equations of all lines having slope 2 and being tangents to the Curve y+ 2 / x-3 =0
Q19(ii)
Find the equations of all lines having slope 0 and that are tangents to the Curve y= 1 / x2-2x+3 =0
Q20
Find the equation of the tangent to the curve y = x2 -2x +7 which is
Q21(i)
Find the equations of the tangents to the curve y =x3+ 2x -4 which are perpendicular to the line x + 14y + 3 =0
Q21(ii)
Find the equations of the tangents to the curve 3x2-y2=2 which are perpendicular to the line x + 3y=2
Q22
Find the equations of the normals to the curve 3x2 -y2 = 8 which are parallel x+3y=4
Q23
Find the angle of intersection between the following curves
Q24
Prove that the curves y = x2-3x +1 and x(y + 3) =4 intersect at right angles at the point (2,-1)
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