Question

Find the gradient, picture below

Answer 1

Hello,

Answer 13/8

Explanation:

`y=2x+(3)/(√(x) ) \\\\y'=2+6*(-1)/(2) x^{(-3)/(2) }\\\\y'=3-(3)/(√(x^3)) \\\\\\For x=4, \\\\y'(4)=2-(3)/(8) =(13)/(8)`

Answer 2

`(dy)/(dx) = (13)/(8)`

Explanation:

`y = 2x + 6 {x}^{ - (1)/(2) } \\ (dy)/(dx) = 2 + 6( - (1)/(2)) {x}^{ - (1)/(2) - 1 } \\ (dy)/(dx) = 2 - 3 {x}^{ - (3)/(2) } \\ (dy)/(dx) = 2 - \frac{3}{ \sqrt{ {x}^(3) } }`

When x = 4,

`(dy)/(dx) = 2 - \frac{3}{ \sqrt{ {4}^(3) } } \\ = (13)/(8)`