Answer:
x = 13
Step-by-step explanation:
Given: f ( x ) = 4.5 x 2 − 3 x + 2 To determine the critical points, we must first calculate the first derivative of the function.
Differentiate the given function with respect to x using the power rule of differentiation, d d x x n = n x n − 1.
f ′ (x) = d (4.5 x 2 − 3 x + 2)
______
d x
Apply sum rule: d d x (f(x)) + g (x) = d d x f (x) + d d x g (x) } f ′ ( x) = d d x (4.5 x^2) + d d x (−3 x) + d d x (x) f ′ (x) = 9 x − 3
To determine the critical points, set f ′ (x) = 0 . 9 x − 3 = 0 9 x = 3 {∴ x = 13}
Therefore, the tangent line to f(x) is horizontal at the point x = 13
Hope this helps, have a nice day/night! :D
