Rate of a reaction increases with the rise of temperature. The reason is

Options

A. `csqrt(ab)`
B. `2csqrt(ab)`
C. `-csqrt(ab)`
D. `-2csqrt(ab)`

Answer

B

Explanation

Given curve is
`xy=c^(2)impliesy=(c^(2))/x`
Let `f(x)=ax=by=ax+(bc^(2))/x`
On differentiating w.r.t `x` we get
`f'(x)=a-(bc^(2))/(x^(2))`
For a maximum put `f'(x)=0`
`implies ax^(2)-bc^(2)=0`
`impliesx^(2)=(bc^(2))/aimpliesx=+-csqrt(b/a)`
Again, differentiating `f"(x)=(2bc^(2))/(x^(3))`
At `x=c sqrt(b/a),f"(x)gt0`
`:.f(x)` is minimum at `x=csqrt(b/a)`
The minimum value at `x=csqrt(b/a)` is
`f(csqrt(b/a))=acsqrt(b/a)+(bc^(2))/csqrt(a/b)`
`=(abc+abc)/(sqrt(ab))=(2abc)/(sqrt(ab))`
`=2csqrt(ab)`