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#### Let 'a' be a real number such that the function is increasing in and decreasing in . Then the function has aOption: 1 Option: 2 Option: 3 Option: 4 increasing in & decreasing in

As is linear, so

Now,

It is a downward parabola, so it will have maximum at

So maximum at

Hence, the correct answer is option (1)

#### Find the point on the curve which is nearest to the point (2, 1).   y=2 has minima ## Crack CUET with india's "Best Teachers"

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• Faculty Support #### Find the slope of tangent to the curve at   Hence the slope of the tangent is zero.

#### Find the minimum value of (ax + by), where    ## Crack NEET with "AI Coach"

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• Faculty Support #### Find the slope of the tangent to the curve   #### If , then find the approximate value of f(2.1).     ## Crack JEE Main with "AI Coach"

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• Faculty Support #### Show that the function decreases in the intervals For f(x) decreases

#### Find the dimensions of the rectangle of perimeter 36 cm which will sweep out a volume as large as possible, when revolved about one of its side. Also, find the maximum volume.

Let the sides of the rectangle are x cm and y cm.

Perimeter = 36 cm

2x + 2y = 36

y = 18 -x

Diffentiate w.r.t. x

For critical point

For minima and maxima

It has maximum volume at x = 12 cm.

Hence the dimension of the rectangle is 12cm x 6 cm.

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• Faculty Support #### Find the intervals on which the function is (a) strictly increasing (b) strictly decreasing.

(a) strictly increasing

(b) strictly decreasing.

#### Show that the function f defined by is an increasing function for all x > 0.   