Question

find k so that function kx³+5 is decreasing? Answer :- k<0.

Answer 1

we know the minimum value of function we take -1(where the function decreases) , f(x) approaches to -1,take x=-1
f(x=)k(-1)^3+5=0
this implies that k=5.
hence,-5<0.
so the value of K would be 5 .

Answer 2

Answer:

All the negative values of k make the function $kx^3 + 5$ decreasing.

Step-by-step explanation:

Given,

$kx^3 + 5$ is decreasing finction

To find,

"k"

We know that if a function is decreasing then the second order derivative must be less than zero

Let $f(x) = kx^3+5$

We try to find first order derivative of f(x)

i.e. $f'(x) = 3kx^2 + 0$

Similarly finding second order derivative of f(x)

i.e.$f''(x) = 6kx$

Now, the condition for the decreasing function is

$f''(x) < 0$

$\implies6kx < 0\\\implies k < 0$

Therefore, all the negative values of k make the function $kx^3 + 5$ decreasing.

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