Question

If 8^x × 5^(-y) = (0.05)^(-y) × (25)^(-3x/2), then the value of x: y will be?

Answer 1

Answer:

Here,

f(x)=x

3

−6x

2

+9x+15=0

⇒f

′

(x)=3x

2

−12x+9.

For local maxima and minima we must have f

′

(x)=0

Now,

f

′

(x)=0 ⇒3(x

2

−4x+3)=0

⇒3(x−3)(x−1)=0⇒x=3orx=1.

Case. ! when x=3

In this case , when x is slightly less than 3 then f

′

(x)=3(x−3)9x−1) is negative and when x is slightly more than 3 then f

′

(x) is positive.

Thus, f

′

(x) changes from negative to positive as x increases through 3.

So, x=3 is a point of local minimum.

Case 2, when x=1

In this case, when x is slightly less than 1 then f

′

(x)=3(x−3)(x−1) is positive and when x is slightly more than 1 then f

′

(x) is negative.

Thus, f

′

(x) changes sign from positive to negative as x increases through 1.

So, x=1 is a point of local maximum.

Local maximum value =f(1)=19.