The equation of a curve is given by y= 1/6 (2x - 9)^6 . a) Find the x coordinate of the point at which the tangent to the curve is parallel to the x- axis. b) Find the equation of tangent to the curve at x = 5 c) The normal to the curve at x = 5 meets the y axis at point A. Find the coordinates of point A. d) A point S (x,y) moves along the curve with time t. When y = 1/6 , dy/dt = 4 units/s, find the corresponding rate of change of x.

Question

The equation of a curve is given by y= 1/6 (2x - 9)^6 .                                         a) Find the x coordinate of the point at which the tangent to the curve is parallel to the x- axis.                                   b) Find the equation of tangent to the curve at x = 5                                                 c) The normal to the curve at x = 5 meets the y axis at point A. Find the coordinates of point A.                              d) A point S (x,y) moves along the curve with time t. When y = 1/6 , dy/dt = 4 units/s, find the corresponding rate of change of x.

anonymous · Answer

Find the x coordinate of the point at which the tangent to the curve is parallel to the x- axis. 
take the derivative, set it equal to zero and solve for $x$

anonymous · Answer

you got that? you can almost do it in your head

anonymous · Answer

I got x = 4.5

anonymous · Answer

$$y'=(2x-9)^5$$ so it is zero at $x=\frac{9}{2}=4.5$ yes

anonymous · Answer

Alright thnx

anonymous · Answer

Find the equation of tangent to the curve at x = 5 
put $x=5$ in the derivative to find the slope

anonymous · Answer

$$m=(2\times 5-9)^5=1^5=1$$

anonymous · Answer

then use the point - slope formula with $m=1, x_1=5, y_1=\frac{1}{6}$

anonymous · Answer

Okay i got y = 2x - 9/5 is that right

anonymous · Answer

can't be because the slope is 1

anonymous · Answer

$$y-\frac{1}{6}=x-5$$

anonymous · Answer

Okay

anonymous · Answer

Hw about part c and d

anonymous · Answer

The derivative is 2(2x-9)^5 i am sure about it