Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 98

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Let $f (x) = (1 + b^{2}) x^{2} + 2 b x + 1$ and let $m (b)$ be the minimum value of $f (x)$ . As $b$ varies, the range of $m (b)$ is

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Important Questions on Application of Derivatives

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 99

The radius of a right circular cylinder of greatest curved surface which can be inscribed in a given right circular cone is

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 100

The dimensions of the rectangle of maximum area that can be inscribed in the ellipse

{(\frac{x}{4})}^{2} + {(\frac{y}{3})}^{2} = 1

are

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 101

The largest area of a rectangle which has one side on the

x

-axis and the two vertices on the curve

y = e^{- x^{2}}

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 102

The maximum distance of the point

(k, 0)

from the curve

2 x^{2} + y^{2} - 2 x = 0

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 106

Find the value of

x

for which function

f (x) = \int_{- 1}^{x} t (e^{t} - 1) (t - 1) {(t - 2)}^{3} {(t - 3)}^{5} d t

has a local minimum

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 3

Equation of normal drawn to the graph of the function defined as

f (x) = \frac{\sin x^{2}}{x}, x \neq 0 & f (0) = 0

at the origin is

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 4

The line

\frac{x}{a} + \frac{y}{b} = 1

touches the curve

y = b e^{- x / a}

at the point

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 5

The equation of normal to the curve

x^{3} + y^{3} = 8 x y

at point where it is meet by the curve

y^{2} = 4 x

, other than origin is