Question

for the function y=x√x find value of x for which rate of change of y with respect to x is 6?

Answer 1

Answer:

X = 16

Explanation:

$\frac{dy}{dx} = 6 \\ \\ \\ 6 = \frac{dy}{dx} (x \sqrt{x} ) \\ \\ \\ \\ \\ \\ 6 = \frac{d}{dx} x. \sqrt{x} + \frac{d}{dx} \sqrt{x} .x \\ \\ \\ 6 = \sqrt{x} + \frac{x}{2 \sqrt{x} } \\ \\ \\ 6 = \sqrt{x} + \frac{ \sqrt{x} }{2 } \\ \\ \\ 12= 3 \sqrt{x} \\ \\ \\ \sqrt{x} = 4 \\ \\ \\ x = 16$

Answer 2

Answer:

x=16

Explanation:

dy/dx=6--------------given but y=x√x dy/dx=√x/2+√x

6= 3√x/2

√x=4

x=16