Question

Find the maximum values of the
expression, 3^x + 3^1-x, x€R. *
3√2
7√2
2√3
5​

Answer 1

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11th

Maths

Relations and Functions

Introduction to Functions

If m is the minimum value o...

MATHS

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Asked on October 15, 2019 by

Yusuf Sindhu

If m is the minimum value of k for which the function f(x)=x

kx−x

2

is increasing in the interval [0,3] and M is the maximum value of f in [0,3] when k=m, then the ordered pair (m, M) is equal to?

MEDIUM

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ANSWER

f(x)=x

kx−x

2

f

′

(x)=

2

kx−x

2

3kx−4x

2

For ↑f

′

(x)≥0 3kx−4x

2

≥0

kx−x

2

≥0 4x

2

−3kx≤0

x

2

−kx≤0 4x(x−

4

3k

)≤0

x(x−k)≤0 so x∈[0,3] 3−

4

3k

≤0

+ve x≥3 k≥4

minimum value of k is m=4

f(x)=x

kx−x

2

=3

4×3−3

2

=3

3

, M=3

3

.