Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 1>Q 4

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If a variable tangent to the curve $x^{2} y = c^{3}$ makes intercepts $a, b$ on $x$ and $y$ axes respectively, then the value of $a^{2} b$ is

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Important Questions on Application of Derivatives

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 1>Q 5

At any two points of the curve represented parametrically by

x = a (2 c o s t - c o s 2 t), y = a (2 s i n t - s i n 2 t)

, the tangents are parallel to the axis of

x

corresponding to the values of the parameter

t

differing from each other by:

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Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 1>Q 6

The equation of the normal to the curve

y = \sin \frac{π x}{2}

at

(1, 1)

is

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Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 1>Q 7

If the lines

y = - 4 x + b

are tangents to the curve

y = \frac{1}{x}

, then

b =

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Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 1>Q 8

At what points of the curve

y = \frac{2}{3} x^{3} + \frac{1}{2} x^{2}

, tangent makes the equal angle with axis?

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Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 1>Q 9

The point on the curve

x^{2} = 3 - 2 y,

where the tangent is parallel to

x + y = 2,

is

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Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 1>Q 10

The equation of the normal to the curve

y (x - 2) (x - 3) - x + 7 = 0

at the point where it cuts the

x

-axis is

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Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 1>Q 11

The equation of the normal to the curve

y = 1 - 2^{\frac{x}{2}}

at the point of intersection with the

Y

-axis is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 1 - Application of Derivatives>Level 1>Q 12

The point on the curve

9 y^{2} = x^{3},

where the normal to the curve makes equal intercepts with the axes, is