Question

Find the point on the curve y= x sqrt (x) where the tangent line is parallel to the line 6x - y = 4

Answer 1

i first found the slope of the line
y= 6x -4

so the slope is 6


the derivative is y' = 3/2 x ^1/2 (using power rule)

and so i did 3/2 x^1/2 = 6

but i couldnt get the correct answer, why?

Answer 2

if it is
\[x\sqrt{x}\] derivative is
\[\frac{3}{2}\sqrt{x}\] then set
\[\frac{3}{2}\sqrt{x}=6\]
\[\sqrt{x}=6\times \frac{2}{3}=4\]
\[x=16\]

Answer 3

ohhhhh i caught my mistake!! thanks