Question

Find K value if f(x)=x+k/x is maximum when x=-2

Answer 1

Answer:

There is a relative minimum when x=2 with k=4, but there is no possible value of k which gives a relative maximum when x=2

Explanation:

Let

f(x)=x+kx

Then differentiating wrt x we get

f'(x)=1−kx2

And differentiating again wrt x we get:

f''(x)=2kx3

the f'(2)=1−k4

At a maximum or minimum we require f'(x)=0, so for a maximum when x=2 we must have f'(2)=0

f'(2)=0⇒1−k22=0
∴1−k4=0
∴k=4

So When k=4⇒f'(x)=0 when x=2giving a single critical point

Now let's find the nature of this critical point. With k=4 and x=2

f''(2)=(2)(4)23>0, Hence this a relative minimum

Answer 2

Hey dear here is your answer!!!!!

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We have been given the value of x = -2.

We would be using the concept of Remainder Theorem to solve this question.

f(x) = $\frac{x+k}{x}$

Substitute the value of 'x':-

When we substitute the value of x as - 2 the equation would be equal to zero as '-2' is the zero of the equation.

$\frac{-2+k}{-2}$ = 0

Transposing:-

-2 + k = 0

k = 2

So, the value of k is 2 when -2 is a zero of the equation !

$\large\boxed{\large\boxed{\large\boxed{Solved !}}}}$

❣️⭐ Hope it helps you dear...⭐⭐❣️❣️