Question

let f(x)=(2/9)x^(3/2) and suppose that the line y=(5/2)x is parallel to the tangent of f(x) at x=a find the value of a. please show all steps!

Answer 1

dydx return the value of gradient of the point .

dy/dx f(x)=1/3x^(1/2)

the second equation show gradient = 5/2 then,

1/3x^(1/2)=5/2
x=15²/2²

Answer 2

So this means to say, at x = a, f'(x) = 5/2.
Differentiating f(x) with respect to x,
f'(x) = sqrt(x)/3
sqrt(x) = 15/2
x = 56.25